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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)

Trigonometry (A) Missing Lengths

Trigonometry (B) Missing Angles and Lengths

Trigonometry (C) Word Problems

Trigonometry (C) Word Problems (With Clues)

3D Trigonometry and Pythagoras (B)

Finding Exact Trig Values

3D Trigonometry and Pythagoras (A)

Area of Triangles

Area of Triangles (With Clues)

Choosing the Correct Trig Rule

Sine Rule Cosine Rule and Area Mixed Exercise

The Cosine Rule

The Sine Rule

Trigonometric Graphs (A)

Trigonometric Graphs (B)

Using Exact Trig Values

Describing Transformations of Trig Graphs

Solving Trigonometric Equations

Transformations of Trig Graphs (A)

Transformations of Trig Graphs (B)

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

Unit 1: right triangles & trigonometry, unit 2: trigonometric functions, unit 3: non-right triangles & trigonometry, unit 4: trigonometric equations and identities, review articles.

Free Math Printable Worksheets with Answer Keys and Activities

Other free resources.

Feel free to download and enjoy these free worksheets on functions and relations. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Long Division with Remainders
• Long Division with Remainders #2 (Zeros in the Quotient)
• Long Division with 2 Digit Divisors
• Whole Number by Unit Fraction
• Equation of Circle
• Simplify Imaginary Numbers
• Adding and Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers
• Dividing Complex Number (Advanced)
• End of Unit, Review Sheet
• Distance Formula
• Simplify Rational Exponents (Algebra 2)
• Solve Equations with Rational Exponents (Algebra 2)
• Solve Equations with variables in Exponents (Algebra 2)
• Exponential Growth (no answer key on this one, sorry)
• Compound Interest Worksheet #1 (No logs)
• Compound Interest Worksheet (Logarithms required)
• Factor Trinomials Worksheet
• Factor by Grouping
• Domain and Range (Algebra 1)
• Functions vs Relations (Distinguish function from relation, state domain etc..) (Algebra 2)
• Evaluating Functions (Algebra 2)
• 1 to 1 Functions (Algebra 2)
• Composition of Functions (Algebra 2)
• Inverse Functions Worksheet (Algebra 2)
• Operations with Functions (Algebra 2)
• Functions Review Worksheet (Algebra 2)
• Logarithmic Equations
• Properties of Logarithms Worksheet
• Product Rule of Logarithms
• Power Rule of Logarithms
• Quotient Rule of Logarithms
• Solve Quadratic Equations by Factoring
• Quadratic Formula Worksheets (3 different sheets)
• Quadratic Formula Worksheet (Real solutions)
• Quadratic Formula (Complex solutions)
• Quadratic Formula (Both real and complex solutions)
• Discriminant and Nature of the Roots
• Solve Quadratic Equations by Completing the Square
• Sum and Product of Roots
• Radical Equations
• Mixed Problems on Writing Equations of Lines
• Slope Intercept Form Worksheet
• Standard Form Worksheet
• Point Slope Worksheet
• Write Equation of Line from the Slope and 1 Point
• Write Equation of Line From Two Points
• Equation of Line Parallel to Another Line and Through a Point
• Equation of Line Perpendicular to Another Line and Through a Point
• Slope of a Line
• Perpendicular Bisector of Segment
• Write Equation of Line Mixed Review
• Word Problems
• Multiplying Monomials Worksheet
• Multiplying and Dividing Monomials Sheet
• Adding and Subtracting Polynomials worksheet
• Multiplying Monomials with Polynomials Worksheet
• Multiplying Binomials Worksheet
• Multiplying Polynomials
• Simplifying Polynomials
• Factoring Trinomials
• Operations with Polynomials Worksheet
• Dividing Radicals
• Simplify Radicals Worksheet
• Adding Radicals
• Multiplying Radicals Worksheet
• Radicals Review (Mixed review worksheet on radicals and square roots)
• Rationalizing the Denominator (Algebra 2)
• Radical Equations (Algebra 2)
• Solve Systems of Equations Graphically
• Solve Systems of Equations by Elimination
• Solve by Substitution
• Solve Systems of Equations (Mixed Review)
• Activity on Systems of Equations (Create an advertisement for your favorite method to Solve Systems of Equations )
• Real World Connections (Compare cell phone plans)
• Identifying Fractions

Trigonomnetry

• 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
• Vector Worksheet
• Sine, Cosine, Tangent, to Find Side Length
• Sine, Cosine, Tangent Chart
• Inverse Trig Functions
• Real World Applications of SOHCATOA
• Mixed Review
• Unit Circle Worksheet
• Graphing Sine and Cosine Worksheet
• Sine Cosine Graphs with Vertical Translations
• Sine, Cosine, Tangent Graphs with Phase Shifts
• Sine, Cosine, Tangent Graphs with Change in Period, Amplitude and Phase Shifts (All Translations)
• Tangent Equation, Graph Worksheet
• Graphing Sine, Cosine, Tangent with Change in Period
• Cumulative, Summative Worksheet on Periodic Trig Functions - period, amplitude, phase shift, radians, degrees,unit circle
• Ratio and Proportion
• Similar Polygons
• Area of Triangle
• Interior Angles of Polygons
• Exterior Angles of Polygons

Arcs and Angles formed by Intersecting Chords

Angles and arcs formed by tangents and secants

Tangents, Secants and Side Lengths

Math Worksheet on the Angle formed by the intersection of a Tangent and a Chord

Cumulative Review Problems of All Formulas

• Associated Powerpoint
• Associated PowerPoint
• System of Linear Equations Worksheet
• System of Linear Equations - Real World Application
• Compositions of Reflections. Reflections Over Intersecting Lines as Rotations

All of these worksheets and activities are available for free so long as they are used solely for educational, noncommercial purposes and are not distributed outside of a specific teacher's classroom.

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Home > Math Worksheets > Ratios > Trigonometric Ratios

We use trigonometric ratios, especially for the measurements of a right triangle. In a right triangle, two sides that make the right angle, we call them legs. The side that is opposite to the right angle is called the hypotenuse. Only three trigonometric ratios are Sine, Cosine, Tangent. To solve the triangle, we have the following formulas; Sine = length of the leg opposite to the angle/length of the hypotenuse (Abbreviated Sin). Cosine = length of the leg adjacent to angle/length of the hypotenuse (Abbreviation Cos). Tangent = length of the leg opposite to the angle/length of the leg to the angle (tan). We have a triangle A.B.C. C.B. is the right angle, B.A. is the hypotenuse, and C.A. is the base. Find angle A. Opposite angle A, the length of a leg is (a). Adjacent to angle A, the length of the leg is (b), and the length of the hypotenuse is (c). The ratio opposite over hypotenuse is the Sine of the angle like; Sin angle A = a/c. The ratio adjacent over hypotenuse, the cosine is; Cos angle A = b/c. The ratio opposite over adjacent, the tangent is; Tan angle = a/b.

For a right triangle, there are six trigonometric ratios: sine, cosine (cos), tangent, cosecant, secant, and cotangent. In these worksheets, students will be working primarily with sine. Your students will be given the value of sides and/or angles of a triangle, and they will then calculate the missing value of a specified side, or the missing value of a specified angle. Diagrams of each triangle the student will be working with are provided as visual aids. Students may require extra paper for their calculations. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. Problems are also provided for students to practice independently. When finished with this set of worksheets, students will be able to solve problems using trigonometric ratios. These worksheets explain how to use trigonometric ratios to find the missing value of a triangle. Sample problems are solved and practice problems are provided.

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Trigonometric ratios worksheets, click the buttons to print each worksheet and answer key., trigonometric ratios lesson.

This worksheet explains how to find the length of a side of a triangle using ratios. A sample problem is solved, and two practice problems are provided.

Students will find all the missing lengths of a missing side of a triangle using ratios. Ten problems are provided.

Using all the information that is given to you in order to find the missing value of a side. Ten problems are provided.

The concept of how to find the length of a side of a triangle using ratios is reviewed. A sample problem is solved and six practice problems are provided.

Students will demonstrate their proficiency with this skill and where they should be going with it. Ten problems are provided.

This is really good to use as a series of exercises to get better. Three problems are provided, and space is included for students to copy the correct answer when given.

Basic trig functions - practice problems

Calculating sine, cosine, and tangent.

• Type 35 into your calculator
• press the sin button.
• Your calculator should read 0.574 . If you do not get the correct answer, check to make sure that your calculator is in degree mode .
• Type 12 into your calculator
• press the cos button.
• Your calculator should read 0.978 .
• Type 75 into your calculator
• press the tan button.
• Your calculator should read 0.0879 .

• Depending on your calculator, you will typically need to press a button labeled 2 nd (sometimes shift) on your calculator and then the sin button. This produces sin -1 on the calculator screen.
• Enter 0.5 after the sin -1 .
• Hit enter or = and the result should be 30 degrees .

Go back to the trig sample problems page

Go back to the trig explanations page.

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Trigonometric Ratios Worksheets

Welcome to the world of trigonometry, "the gateway to engineering", as it is often referred to by our team of experts, for its umpteen real-life applications. Here is a set of meticulously crafted printable trigonometric ratios worksheets for high school students to get their basics right. These trig ratio worksheets feature exercises to identify the legs, side and angles, introduce the six trigonometric ratios, find the indicated sides and much more. Access some of these worksheets for free!

» Primary Trigonometric Ratios

» Reciprocal Trigonometric Ratios

Identify the Sides of the Right Triangle

Spot the two legs- opposite, adjacent and the 3rd side- hypotenuse of the right triangle. The right triangle trigonometry chart comes handy here.

Determine the Six Trigonometry Ratios

This array of pdf worksheets contains skills to find the three primary trigonometric ratios for the given angle, using the SOH-CAH-TOA ; and flip the answers to get the corresponding reciprocal trigonometric ratios.

Find the Trigonometric Ratio

Featured here are worksheets encompassing exercises to find the indicated trigonometric ratio based on the given trig ratio.

Find the Value of Trigonometric Ratios Using Charts

Compiled here are exercises to find the value of trigonometric ratios using the trigonometric ratio tables . The 1st part of the worksheet includes degrees while the 2nd has radians.

Find the Trigonometric Ratios Using a Calculator

Ample practice is provided in finding the values of trig ratios for the given degrees and radians in this range of printable high school worksheets. Usage of a calculator is recommended.

Find the Indicated Side / Perimeter of a Right Triangle Using Trigonometric Ratios

Utilize this array of two-part worksheets, whose first includes exercises to find the labeled side and the 2nd deals with finding the perimeter. The printables are available in customary and metric units.

Raise the bar with these trigonometric ratios pdf worksheets here that contain expressions with a mix of degrees and radians. Learn the trig-ratios from the trigonometric ratio charts and apply them to evaluate the expressions.

Primary Trigonometric Ratios (sin, cos, tan)

For a crystal clear understanding of the primary trigonometric ratios - sin / sine, cos / cosine and tan / tangent, employ these 25+ practice worksheets.

(27 Worksheets)

Reciprocal Trigonometric Ratios

Incorporate this assemblage of tailor-made worksheets to learn the reciprocal trigonometric ratios - cosec / cosecant, sec / secant and cot / cotangent.

Related Worksheets

» Pythagorean Theorem

» Evaluating Trigonometric Expressions

» Trigonometric Identities

» Inverse Trigonometric Ratios

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Definition of trig

 (Entry 1 of 2)

Definition of trig  (Entry 2 of 2)

• uncluttered
• well-groomed

Example Sentences

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'trig.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

by shortening

Middle English, trusty, nimble, of Scandinavian origin; akin to Old Norse tryggr faithful; akin to Old English trēowe faithful — more at true entry 1

circa 1878, in the meaning defined above

1513, in the meaning defined at sense 1

Dictionary Entries Near trig

Cite this entry.

“Trig.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/trig. Accessed 4 Sep. 2023.

Kids Definition

Kids definition of trig.

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trigonometry .

Origin of trig

Words nearby trig.

• trifunctional
• trigeminal nerve

Other definitions for trig (2 of 4)

neat, trim, smart, or spruce.

in good physical condition; sound; well.

to make trim, smart, etc. (often followed by up or out ).

Other words for trig

Other words from trig.

• trigness, noun

Other definitions for trig (3 of 4)

to support or prop, as with a wedge.

to act as a check on (the moving of wheels, vehicles, etc.).

a wedge or block used to prevent a wheel, cask, or the like, from rolling.

Other definitions for trig. (4 of 4)

trigonometric.

trigonometrical.

trigonometry.

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

How to use trig in a sentence

“I think in regard to trig , anything is possible,” McGinniss writes.

Palin dedicates the book to her 2-year old son, trig , who has Down syndrome.

The media frenzy around them was astonishing—they were rock stars, from Bristol and Levi down to little trig .

How could I ever forget the sight of a banner held up high to say “We Are Here For trig ”?

Has Senator McCain simply forgotten that Calculus Algebra trig has Down Syndrome?

Jane was a trig , neat body; small, as the coast girls often are—I wonder why?

Harry and Seth made everything trig and came in last, leaving the cat-boat at anchor far out.

The trig little sail-boat turned out to be a respectable yacht, steam, at that.

trig ′amist, one who marries three wives; trig ′amy, the state of having three husbands or wives at the same time.

Trigla, trig ′la, n. the typical genus of Triglid, the gurnards.

British Dictionary definitions for trig (1 of 3)

/ ( trɪɡ ) archaic , or dialect /

neat or spruce

to make or become trim or spruce

Derived forms of trig

• trigly , adverb
• trigness , noun

British Dictionary definitions for trig (2 of 3)

/ ( trɪɡ ) mainly dialect /

a wedge or prop

to block or stop

to prop or support

British Dictionary definitions for trig. (3 of 3)

trigonometrical

trigonometry

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

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