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Trigonometry Worksheets

Maths Worksheets / Trigonometry Worksheets

Trigonometry is a mathematical method used to define relations between elements of a triangle. Our maths trigonometry worksheets with answers will help your child or student to grasp and understand basic and more advanced ways of solving trigonometric equations. Our comprehensive resources include Pythagoras and trigonometry worksheets with answers, trigonometry area of triangle worksheets and transformations of trig graphs worksheets – all designed to make trigonometry fun and interesting.

Discovering Trigonometry (Investigation)

Discovering Trigonometry (Investigation) Worksheet created for students in KS3

Trigonometry (A) Missing Lengths

Trigonometry Missing Lengths Worksheet fit for students in year 8 and year 9

Trigonometry (B) Missing Angles and Lengths

Trigonometry Missing Angles and Lengths Worksheet perfect for students in year 8 and year 9

Trigonometry (C) Word Problems

Trigonometry Word Problems Worksheet fit for students in year 8 and year 9

Trigonometry (C) Word Problems (With Clues)

Trigonometry Word Problems (With Clues) Worksheet suitable for students in KS3

3D Trigonometry and Pythagoras (B)

3D Trigonometry and Pythagoras Worksheet fit for students in year 10 and year 11

Finding Exact Trig Values

Cazoom-Maths.-Trigonometry.-Finding-Exact-Trig-Values

3D Trigonometry and Pythagoras (A)

3D Trigonometry and Pythagoras Worksheet suitable for students in KS4

Area of Triangles

Area of Triangles Worksheet perfect for students in year 10 and year 11

Area of Triangles (With Clues)

Area of Triangles (With Clues) Worksheet fit for students in year 7 and year 8

Choosing the Correct Trig Rule

Choosing the Correct Trig Rule worksheet suitable for students in year 10 and 11

Sine Rule Cosine Rule and Area Mixed Exercise

Sine Rule Cosine Rule and Area Mixed Exercise Worksheet created for students in KS4

The Cosine Rule

The Cosine Rule Worksheet perfect for students in year 10 and year 11

The Sine Rule

The Sine Rule and Area of Triangles Worksheet created for students in KS4

Trigonometric Graphs (A)

Trigonometric Graphs Worksheet created for students in KS4

Trigonometric Graphs (B)

Trigonometric Graphs Worksheet suitable for students in KS4

Using Exact Trig Values

Cazoom-Maths.-Trigonometry.-Using-Exact-Trig-Values.

Describing Transformations of Trig Graphs

Describing Transformations of Trig Graphs Worksheet created for students in KS4

Solving Trigonometric Equations

Solving Trigonometric Equations Worksheet perfect for students in year 11 and year 12

Transformations of Trig Graphs (A)

Transformations of Trig Graphs Worksheet fit for students in year 11 and year 12

Transformations of Trig Graphs (B)

Transformations of Trig Graphs Worksheet perfect for students in year 11 and year 12

Printable Trigonometry Worksheets with Answers

Why is trigonometry important.

When learning about trigonometry, many students struggle to understand how it is relevant in real life.

Studying the properties of triangles and calculating missing angles can seem like an arbitrary task, but it actually has many applications in the real world. From astronomy, to aviation, medicine and more, trigonometry allows many industries to function.

Essential Knowledge for Future Scientists

A solid knowledge of trigonometry is essential for any student who aspires to work in a scientific discipline.

Students will need to master trigonometry at GCSE level in order to study A-Level maths and sciences, subjects which they will need to secure a university place for engineering, medicine, and the sciences. Although many computer applications perform trigonometric calculations automatically, all the staff working in these industries will have an excellent knowledge of trigonometry and use it regularly.

Nurture Students’ Transferable Skills

Even if students do not wish to pursue a career in these technical and scientific fields, practicing trigonometry questions helps them develop transferable skills valued by all employers.

Using Trigonometry improves students’ problem solving abilities and promotes critical thinking, skills which will prove useful throughout their studies and into adult life. Providing students with trigonometry worksheets helps to nurture these skills, allowing them to be successful not just at their maths exams but right the way through their career.

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Trigonometry Worksheets (Missing Angles)

Related Pages Math Worksheets Free Printable Worksheets

Trigonometry Worksheets

There are six sets of Trigonometry worksheets:

  • Sin, Cos, Tan
  • Sin & Cos of Complementary Angles
  • Find Missing Sides
  • Find Missing Angles
  • Area of Triangle using Sine
  • Law of Sines and Cosines

Find Missing Angles Worksheets

In these free math worksheets, students learn to find missing angles in right triangles using Trigonometry.

There are two sets of find missing angles worksheets: Find missing angles of triangles Missing angles word problems

How to find missing angles using Trigonometry? Trigonometric functions have inverse functions known as arcsin (or inverse sine), arccos (or inverse cosine), and arctan (or inverse tangent). These inverse functions are denoted as sin -1 , cos -1 , and tan -1 , respectively. These functions help find angles when you know certain trigonometric ratios.

Arcsin The arcsin function, also known as the inverse sine function, is the inverse of the sine function. It takes a number between -1 and 1 as input and returns the angle whose sine is equal to that number. For example, arcsin(0.5) = 30 degrees, because sin(30 degrees) = 0.5.

Arccos The arccos function, also known as the inverse cosine function, is the inverse of the cosine function. It takes a number between -1 and 1 as input and returns the angle whose cosine is equal to that number. For example, arccos(0.866) = 30 degrees, because cos(30 degrees) = 0.866.

Arctan The arctan function, also known as the inverse tangent function, is the inverse of the tangent function. It takes a number as input and returns the angle whose tangent is equal to that number. The arctan function can take any real number as input, but its output will always be between -90 degrees and 90 degrees. For example, arctan(1) = 45 degrees, because tan(45 degrees) = 1.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Trigonometry (Missing Angles) Worksheets .

Missing Angles Worksheet

More Trigonometry (Missing Angles) Worksheets

Printable (Answers on the second page.) Missing Angles Worksheet #1 Missing Angles Worksheet #2

Online Trigonometry (sine, cosine, tangent) Trigonometry (sine, cosine, tangent) Trigonometry (using a calculator) Inverse Trigonometry (using a calculator) Trigonometry (find an unknown side) Trigonometry (find an unknown angle) Using Sine Using Cosine Using Tangent Using Sine, Cosine or Tangent Trigonometry Applications Problems Law of Sines or Sine Rule Law of Sines Law of Cosines or Cosine Rule Law of Cosines

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Trigonometry Worksheets

Trigonometry worksheets promote an understanding of trigonometry concepts. Students can use these worksheets to improve their skills in solving trigonometric problems. The questions included in the worksheet are based on solving trigonometric identities, deriving trigonometry formulas, understanding trigonometry elements such sines, cosines, etc.

Benefits of Trigonometry Worksheets

Trigonometry finds use in several real life applications such as architecture, music, data analysis, etc. Hence, students must be well versed in the topic. This can only happen with clear concepts and immense practice that is provided by trigonometry worksheets.

As the scope of trigonometry is very vast, thus the worksheets have a gradual increase in the level of difficulty. This makes sure that a student doesn't get confused and can assimilate information effectively. Another added feature of these worksheets is that they are flexible, enabling students to work at their own pace.

Download Trigonometry Worksheet PDFs

They combine fun with studies so that students can have a holistic learning experience.These math worksheets should be practiced regularly and are free to download in PDF formats.

MATH Worksheets 4 Kids

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Primary Trig Ratios Worksheets | Sine, Cosine, Tangent

Practice these assortments of primary trigonometric ratio worksheets designed to benefit high school children with topics like finding trigonometric ratios using SOH-CAH-TOA; determine all the three primary trigonometric ratios of the right-angled triangle; find the value of sine, cosine and tangent; and more. Our free trigonometric ratios worksheets are definitely worth a try!

Primary Trigonometric Ratios Using Segments

Primary Trigonometric Ratios Using Segments

These printable worksheets require students to use SOH-CAH-TOA to find the trigonometric ratios sin θ, cos θ and tan θ.

  • Download the set

Primary Trigonometric Ratios Using Lengths | Customary

Primary Trigonometric Ratios Using Lengths

The sides of the right-angled triangle are given in these pdf worksheets. Determine the value of the given trigonometric ratio. The skill is offered in both customary and metric units.

Find sin, cos, tan: Level 1

Find sin, cos, tan: Level 1

All the three sides of a right-angled triangle are given. Find the value of sine, cosine and tangent for the specified angle.

Find sin, cos, tan: Level 2 | Customary

Find sin, cos, tan: Level 2

Apply Pythagorean theorem to determine the missing length of a right-angled triangle. Find all the three primary trigonometric ratios using the information provided.

Indicated Primary Trigonometric Ratio

Indicated Primary Trigonometric Ratio

Each problem contains a trigonometric ratio. Determine the value of the indicated trigonometric ratio. Ex: Find sin θ if cos θ = 3/5.

Solve Using Calculator

Solve Using Calculator

Use calculator to determine the value of sine, cosine or tangent. Each printable high school worksheet consists of two sections, Part-A and Part-B that offers problems in degrees and radians respectively.

Evaluate Trigonometric Expressions

Evaluate Trigonometric Expressions

Evaluate the expressions in these pdf worksheets by identifying the values of the given trigonometric ratios. The angles are specified in degrees or radians.

Related Worksheets

» Pythagorean Theorem

» Trigonometry Charts

» Reciprocal Trigonometric Ratios

» Trigonometric Ratios

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Inverse Trig Functions Worksheet (pdf) and Answer Key

Students will practice determing angles of right triangles by using inverse trig functions -- arcsine, arc cos, arc tan.

Example Questions

Example Question

Other Details

This is a 4 part worksheet:

  • Part I Model Problems
  • Part II Practice
  • Part III Challenge Problems
  • Part IV Answer Key
  • All Things Sine, Cosine and Tangent : links, youtube vids, formulas etc..
  • Arcsine, Arcos, Arctan
  • Using SOHCAHTOA to Find Side Length of a Right Triangle

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  • Finding the Side Length of a Right Triangle SOHCAHTOA vs Pythagorean Theorem

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Surface area of a Cylinder

Trigonometry in Right Angled Triangles (SOH CAH TOA): Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

Mathster keyboard_arrow_up Back to Top

Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.

Corbett Maths keyboard_arrow_up Back to Top

Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.

Trigonometric Identities

Trigonometric Identities

Trigonometric Identities Problems & Solver Worksheet in PDF Format

The Basic 8 Trig Identities Worksheet with Answers

The Basic 8 Trig Identities Worksheet with Answers offers a valuable resource for students and enthusiasts looking to master trigonometry. Trigonometric identities play a crucial role in solving complex mathematical problems involving angles and triangles. This worksheet provides a collection of practice questions, accompanied by step-by-step solutions, allowing you to reinforce your knowledge of the eight fundamental trigonometric identities. Strengthen your understanding of trigonometry and enhance your problem-solving skills with this comprehensive worksheet.

The Basic 8 Trig Identities

Trigonometric identities are equations that relate the angles and lengths of triangles to the values of trigonometric functions. The basic 8 trig identities are foundational equations that play a crucial role in solving trigonometric problems and proving more complex identities. These identities are derived from the ratios of the sides of right triangles and are used extensively in trigonometry and calculus.

The Basic 8 Trig Identities

The first four basic trig identities involve the three primary trigonometric functions: sine (sin), cosine (cos), and tangent (tan). The remaining four identities are derived from the reciprocal functions: cosecant (csc), secant (sec), and cotangent (cot).

The basic 8 trig identities are as follows:

  • sin²θ + cos²θ = 1
  • 1 + tan²θ = sec²θ
  • 1 + cot²θ = csc²θ
  • cscθ = 1/sinθ
  • secθ = 1/cosθ
  • cotθ = 1/tanθ
  • tanθ = sinθ/cosθ
  • cotθ = cosθ/sinθ

Eight Fundamental Trigonometric Identities

Trigonometric identities are mathematical equations that establish relationships between the angles and lengths of triangles and the values of trigonometric functions. The eight fundamental trigonometric identities form the basis for more complex trigonometric identities and equations. These identities are derived from the ratios of the sides of right triangles and are widely used in various branches of mathematics, physics, and engineering.

Eight Fundamental Trigonometric Identities

The fundamental trigonometric identities are divided into two categories: the Pythagorean identities and the reciprocal identities.

Pythagorean Identities:

Reciprocal Identities: 4. cscθ = 1/sinθ

The Pythagorean identities relate the squares of sine, cosine, and tangent to each other, while the reciprocal identities express the trigonometric functions in terms of their reciprocals. These identities enable the simplification of trigonometric expressions, the solution of trigonometric equations, and the conversion between different trigonometric functions.

By understanding and applying these fundamental trigonometric identities, mathematicians and scientists can analyze and solve a wide range of problems involving angles, triangles, and periodic phenomena.

Basic 8 Trig Identities Worksheet with Answers

Below is a worksheet that provides practice problems for the basic 8 trig identities. Use the given identities to simplify the trigonometric expressions and write the answers in terms of sine, cosine, and tangent functions.

Basic 8 Trig Identities Worksheet with Answers

  • Simplify the expression: sin²θ + cos²θ
  • Simplify the expression: 1 + tan²θ

Answer: sec²θ

  • Simplify the expression: 1 + cot²θ

Answer: csc²θ

  • Simplify the expression: cscθ * sinθ
  • Simplify the expression: secθ * cosθ
  • Simplify the expression: cotθ * tanθ
  • Simplify the expression: sinθ / cosθ

Answer: tanθ

  • Simplify the expression: cosθ / sinθ

Answer: 1/tanθ

By practicing these problems, you will become more familiar with the basic 8 trig identities and gain confidence in using them to simplify and manipulate trigonometric expressions.

What Are the Basic Trigonometric Identities?

The basic trigonometric identities are a set of fundamental equations that relate the angles and lengths of triangles to the values of trigonometric functions. These identities are derived from the ratios of the sides of right triangles. And serve as the building blocks for more complex trigonometric equations and formulas. The basic trigonometric identities include:

  • sin²θ + cos²θ = 1: This identity states that the square of the sine of an angle plus the square of the cosine of the same angle equals 1.
  • 1 + tan²θ = sec²θ: This identity states that the square of the tangent of an angle plus 1 equals the square of the secant of the same angle.
  • 1 + cot²θ = csc²θ: This identity states that the square of the cotangent of an angle plus 1 equals the square of the cosecant of the same angle.
  • cscθ = 1/sinθ: This identity states that the cosecant of an angle is equal to the reciprocal of the sine of the same angle.
  • secθ = 1/cosθ: This identity states that the secant of an angle is equal to the reciprocal of the cosine of the same angle.
  • cotθ = 1/tanθ: This identity states that the cotangent of an angle is equal to the reciprocal of the tangent of the same angle.
  • tanθ = sinθ/cosθ: This identity states that the tangent of an angle is equal to the ratio of the sine of the angle to the cosine of the same angle.
  • cotθ = cosθ/sinθ: This identity states that the cotangent of an angle is equal to the ratio of the cosine of the angle to the sine of the same angle.s

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IMAGES

  1. Right Triangle Trigonometry Worksheets

    trig worksheet with answers

  2. Right Triangle Trig Review Worksheet Answers

    trig worksheet with answers

  3. Trigonometric Identities Worksheet With Answers

    trig worksheet with answers

  4. Kuta Software Infinite Geometry Trigonometry Answer Key

    trig worksheet with answers

  5. Solving Trigonometric Equations Worksheet With Answers

    trig worksheet with answers

  6. Trig Identities Worksheet With Answers

    trig worksheet with answers

VIDEO

  1. Trig Word Problems Worksheet

  2. Trig Solve a Right Triangle

  3. Worksheet 11.2 Trig Equations ALL Solutions

  4. Graphing Trig Functions

  5. Inverse Trig Functions

  6. Worksheet [2] Trig. 1st Secondary

COMMENTS

  1. Trigonometry Worksheets (pdf) with answer keys. Download print and enjoy!

    Plus each one comes with an answer key. Law of Sines and Cosines Worksheet. (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle) Law of Sines. Ambiguous Case of the Law of Sines. Law Of Cosines.

  2. PDF Right Triangle Trig Missing Sides and Angles

    Right Triangle Trig. - Finding Missing Sides and AnglesDate_____ Period____ ... Round answers to the nearest tenth. 17) ... 0 0 1AwlWl5 ar6i mgsh zt3sc xr 8e6s Ve4rBv WeldC. G w aMda rd Rec 1w8iJtGhg nIunQfBiln hi AtMeh yA 3llgne AbBrMas b2C.Y Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Right Triangle Trig. ...

  3. Trigonometry Worksheets (worksheets, printable, online, answers)

    How to find trigonometry ratios sine, cosine, and tangent. Trig Ratios. Free Printable and Online Worksheet with answers. opposite, adjacent and hypotenuse. Practice Worksheets for Geometry and Trigonometry.

  4. Trigonometry Worksheets

    Trigonometry Worksheet Answer Page. Now you are ready to create your Trigonometry Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. This Trigonometry Worksheet will produce problems for solving right triangles. This worksheet is a great resource for the 5th Grade, 6th Grade, 7th Grade, and 8th ...

  5. PDF Trigonometry to Find Angle Measures

    Trigonometry to Find Angle Measures. 3) tan Y = 0.6494. 5) cos V = 0.6820. 2) cos Z = 0.1219. 4) sin U = 0.8746. 6) sin C = 0.2756. Find the measure of the indicated angle to the nearest degree. 7) ©0 c2209172o 8KGuQtvae 1S8orfLtEwbaWrAeC xLnLECx.R R GAclfl1 ArwingyhztTsh 1rceXs7enrYvJeldj.5 U tMvajdjed rwqiEtHhg 5Ionrf1iNngiItue3 ...

  6. Trigonometry Worksheets (Math Made Fun)

    Printable PDF Trigonometry Worksheets with Answers. At Cazoom Math, we create a variety of Math trigonometric worksheets that will be sure to meet the needs of your High School child. We have also provided answer keys to all our worksheets, so your child can build confidence in working within triangle concepts.

  7. Trigonometry Worksheets

    Trigonometry Worksheets for High School. Explore the surplus collection of trigonometry worksheets that cover key skills in quadrants and angles, measuring angles in degrees and radians, conversion between degrees, minutes and radians, understanding the six trigonometric ratios, unit circles, frequently used trigonometric identities, evaluating ...

  8. PDF Trigonometry To Find Lengths

    50.7. 61.5. Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. ©p 92r0l1T2D yKguitoaa BSEoaf6t2w3adrgez NLJLoCW.U K jASl1lO crPiTgKhFtPsd wrVeysveorUvyeCde.b 4 KMEaod6e6 twhiMtohI JIIncfKidnniot3ep ZAIlPg3elbzrTax Q1R.T.

  9. Trigonometry

    Trigonometric ratio: SOH (because we are looking for the opposite side) Equation: sin (30°) = Opposite / 10. Solve: Opposite = 10 * sin (30°) = 5 cm. Example 2: Given a right triangle with an adjacent side of 6 cm and an angle of 45°, find the length of the hypotenuse. Solution: Known side: Adjacent = 6 cm.

  10. Trigonometry Practice Questions

    Click here for Answers. . Answers - Version 1. Trigonometry Answers Version 1 - Corbettmaths. Watch on. Answers - Version 2. Trigonometry Answers Version 2 - Corbettmaths. Watch on. Practice Questions.

  11. Trigonometry Worksheets

    At Cazoom Maths we provide a trigonometry worksheet for every question your student might encounter, from a sine and cosine rule worksheet with answers, special triangles worksheet and 3d trigonometry worksheet questions and answers. Your student will have no fear of angles and triangles with the help of our Cazoom Maths Trigonometry worksheets.

  12. Trigonometry

    How to find missing angles of a right triangle using Trigonometry, Arcsin, Arccos, Arctan. find missing angles in right triangles. Free Printable and Online Worksheet with answers. Practice Worksheets for Geometry and Trigonometry.

  13. Geometry Worksheets

    This Trigonometry Worksheet will produce multi-step trigonometric problems. This worksheet is a great resource for the 5th Grade, 6th Grade, 7th Grade, and 8th Grade. These Trigonometry Worksheets allow you to select different variables to customize for your needs. These Geometry worksheets are randomly created and will never repeat.

  14. Download Free Trigonometry Worksheet PDFs

    Download Trigonometry Worksheet PDFs. They combine fun with studies so that students can have a holistic learning experience.These math worksheets should be practiced regularly and are free to download in PDF formats. Trigonometry Worksheet - 1. Download PDF. Trigonometry Worksheet - 2. Download PDF. Trigonometry Worksheet - 3.

  15. PDF I NAME DATE 6,-1 Practice W rksheet

    6,-1 Practice Worksheet Graphs of the Trigonometric Functions Find each value by referring to the graphs of the trigonometric functions. 1. sin (-720 °) 2. tan (-180 °) 3. cos (540 °) 4. tan (180 °) 5. csc (720 °) 6. sec (180 °) Find the values of _ for which each equation is true. 7. sin 0 =-1 8. sec _ =-1 9. tan O= 0

  16. Primary Trig Ratios Worksheets

    Find sin, cos, tan: Level 1. All the three sides of a right-angled triangle are given. Find the value of sine, cosine and tangent for the specified angle. Download the set. Find sin, cos, tan: Level 2. Apply Pythagorean theorem to determine the missing length of a right-angled triangle. Find all the three primary trigonometric ratios using the ...

  17. PDF Trigonometry Worksheet T1

    Trigonometry Worksheet T3 - Calculating Sides Work out the sides labelled. Questions 1 and 2 require Sine, questions 3 and 4 require Cosine, question 5 and 6 require Tangent. The rest …. you will need to work out which to use and how! (Worksheet T1 may help you!!) 1. 7. 2. 8. 3. 9. 4. 10. 5. 11. 6. 12.

  18. Inverse Trig Functions Worksheet (pdf) and Answer Key

    Free worksheet(pdf) and answer key on finding angles of right triangles using inverse sine, cosine and tangent. scaffolded questions that start relatively easy and end with some real challenges. Plus model problems explained step by step

  19. PDF Graphs of Trig Functions

    Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus Graphs of Trig Functions Name_____ Date_____ Period____-1-Find the amplitude, the period in radians, the phase shift in radians, the vertical shift, and the minimum and maximum values. Then sketch the graph using radians. 1) y sin

  20. PDF Trigonometric Identities & Solving Trig Equations

    4.18 Review Worksheet: Trig Inverses & Principal Values Date: Find the exact value for each expression. Use radian measures for angles. Use principal values for inverses. 1. ... Give answers in degrees. Inverse Sine 1. Find Sin-1 (1 2), a) without a calculator _____ b) with a calculator (check your mode!) _____ 2.

  21. Mr Barton Maths

    Trigonometry in Right Angled Triangles (SOH CAH TOA): Worksheets with Answers. Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers. Contents. Mathster; Corbett Maths

  22. The Basic 8 Trig Identities Worksheet with Answers

    Below is a worksheet that provides practice problems for the basic 8 trig identities. Use the given identities to simplify the trigonometric expressions and write the answers in terms of sine, cosine, and tangent functions. Simplify the expression: sin²θ + cos²θ. Answer: 1. Simplify the expression: 1 + tan²θ. Answer: sec²θ.

  23. PDF Practice Problems: Trig Integrals (Solutions)

    Now combine the two answers and add C: Z cot3 xdx= 1 2 csc2 x+ lnjsinxj+ C 13. R sin8xcos5xdx Solution: I don't think you would see a problem like this on your exam, but it is nice to practice anyway. There is a trig identity listed on page 476 of your text: sinAcosB = 1 2 [sin( A B) sin( + )]. You can also derive this equation yourself. Z ...