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• Addition Formulas
• Derivatives of Trig Functions
• Double/Half Angle Formulas
• Full List of Trigonometric Identities
• Magic Identity
• Basic Trigonometry
• Measuring an Angle
• Product and Sum Formulas
• Pythagorean Identities
• Right Angle Trig
• Tangents and Slope
• Trig Functions
• What is Trigonometry?

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Trigonometry Cheat Sheet: Ace your Exam with This Study Guide

• Kayla Griffin
• Categories : Help with math homework
• Tags : Homework help & study guides

Before you start reading, you should know that this is only a review. If you don’t have any experience with the subject, there is not enough information here to teach it to you. For those of you that have studied the material before, this is a condensed formula sheet to help you prepare for exams. It is also helpful as a handy homework reference.

Until now, you probably measured angles in degrees. Most of trig uses radians.

Unit Circle

The unit circle is segmented into 360 degrees or 2*pi radians. (For this article, p will denote pi=3.14159…)

90 degrees = p/2 radians

180 degrees = p radians

0 degrees = 0 radians = 2p radians = 360 degrees (Note that 0 and 2p are often used interchangeably)

The unit circle below gives the commonly used angles and their sines/cosines.

If Θ is an angle made by connecting (0,0), (1,0) and any other point on the unit circle M = (a,b), then cosΘ = a, sinΘ = b, or equivalently: (a,b) = (cosΘ, sinΘ)

For example: the line for Θ=p/4 radians crosses the circle at (sqrt(2)/2, sqrt(2)/2). Therefore x = cos Θ = sqrt(2)/2 = y =sinΘ, or equivalently: (sqrt(2)/2, sqrt(2)/2) = (cos(p/4), sin(p/4)).

Negative Angles

Counterclockwise movement on the unit circle is measured in positive units and clockwise movement is measured in negative units. Therefore, the distance from p to 2p can also be notated as 0 to -p, depending on which way you travel the circle.

Relationships between angles are important:

Supplementary Angles: x+y = p = 90 degrees

Complementary Angles: x+y = 2p = 180 degrees

For the purpose of the trig cheat sheet, and conventionally, if the sides of a triangle are labeled a, b, c then the angles are ABC, where A is the angle made by b and c, B is the angle made by a and c, and C is the angle made by a and b. A is called the opposite angle of a, and a is the opposite side of A.

Much of trigonometry is based on triangles, usually right or acute.

Triangle area formulas:

½*base*height=Area

½*a*b*sinC=Area

½*b*c*sinA=Area

½*c*a*sinB=Area

s*(s-a)*(s-b)*(s-c)=(a+b+c)*(b+c)*(a+c)*(a+b)=Area^2 [s=a+b+c]

More With Triangles

This trig cheat sheet uses Θ, A and B to represent angles. Your notes or textbook may use x and y or other variables, but the meanings are the same.

Right Triangle and Sine, Cosine, Tangent

An easy pneumonic for the sine, cosine, tangent right triangle definitions is SOHCAHTOA . This stands for S ine= O pposite/ H ypotenuse ( SOH ); C osine= A djacent/ H ypotenuse ( COH ); T angent= O pposite/ A djacent ( TOA ).

The chart below gives a breakdown of the trig functions and their relationship to right triangles and the unit circle.

Here is a simple way to remember the right triangle relationships: Hold up your left hand, palm facing out, fingers together and thumb sticking out the right like an L. Now, imagine a line from the tip of your forefinger to the tip of your thumb. If you pretend the curve where your thumb meets your hand is a right angle, then you have a right triangle. Your thumb is a, your forefinger is b, and the imaginary line (the hypotenuse) is c. Then the angle at the tip of your forefinger is A, the tip of your thumb is B and the right angle is C. Now, use that to memorize the following definitions:

sinA=opp/hyp = a/c

cosA=adj/hyp= b/c

tanA=opp/adj = a/b

cscA = hyp/opp = c/a = 1/sinA

secA = hyp/adj = c/b = 1/cosA

cotA = adj/opp = c/b = 1/tanA

Laws and Theorems

The trig cheat sheet only gives the formulas for these theorems. If you are required to use the full definition, or are unsure when to use each formula, you will need additional study material.

Pythagorean Theorem, Law of Sines, Law of Cosines, Law of Tangents are all about the relationships between the sides and angles of triangles.

~ Pythagorean theorem (only for right triangles with sides a, b, c, where c is the hypotenuse):

Using the definition of a right triangle on your hand (as explained above) the lengths of the sides are related by the following formula:

a2 +b2 = c2

~ Law of sines (for all triangles with sides lengths a, b, c and with angles A, B, C)

sin(A)/a = sin(B)/b = sin(C)/c

~ Law of cosines (for all triangles with sides lengths a, b, c and with angles A, B, C)

c²=a²+b²-2*a*b*cos(C)

b²=a²+c²-2*a*c*cos(B)

a²=b²+c²-2*b*c*cos(A)

When the angle C is p, 0, or 2p, the law of cosines reduces to a simpler formula. If it is easier for you to memorize these too, go ahead, but usually I just solve for them.

When C = p: c²=a²+b² (the Pythagorean theorem)

When C=0, cos(0)=1: c2 = (a-b)2

When C=2p, cos(2)=-1: c 2 = (a+b)2

~ Law of Tangents (for all triangles with sides a, b, c and with angles A, B, C)

(a+b)/(a-b) = [tan(1/2(A+B))]/[tan(1/2(A-B))]

Important Trig Formulas (More Memorization)

Here is a list of the most important trig formulas. It is best to memorize as many as you can, but remember that some can be derived from others (if that’s easier for you) and many are related. The trig cheat sheet uses Greek letters such as Θ to represent angles. Please note that where marked below, a and b are angles, and p represents pi=3.14159….

Squared formulas

sin2(Θ)+cos2(Θ)=1

1+tan2(Θ) = sec2(Θ)

1+cot2(Θ) = csc2(Θ)

sin(-Θ) = -sinΘ

cos(-Θ) = cosΘ

tan(-Θ) = -tanΘ

Periodic Functions (p = pi = 3.14159…)

sin(Θ) = sin(Θ+2kp)

cos(Θ) = cos(Θ+2kp)

where k is any integer, positive or negative.

Sum and Difference formulas (a and b are angles)

sin(a+b)=sin(a)cos(b)+sin(b)cos(a)

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

tan(a+b)=[tan(a)+tan(b)]/[1-tan(a)tan(b)]

sin(a-b)=sin(a)cos(b)-sin(b)cos(a)

cos(a-b)=cos(a)cos(b)+sin(a)sin(b)

tan(a-b)=[tan(a)-tan(b)]/[1+tan(a)tan(b)]

tan([a+b]/2) = [sin(a)+sin(b)]/[cos(a)+cos(b)] = -[cos(a)-cos(b)]/[sin(a)-sin(b)]

Power Reduction Formulas

sin2(Θ) = [1-cos(2Θ)]/2

cos2(Θ) = [1+cos(2Θ)]/2

Product to Sum Formulas (a and b are angles)

cos(a)cos(b) = ½[cos(a-b) + cos(a+b)]

sin(a)sinb() = ½ [cos(a-b) – cos(a+b)]

sin(a)cos(b) = ½[sin(a+b) + sin(a-b)]

cos(a)sin(b) = ½[sin(a+b) – sin(a-b)]

Sum to Product Formulas (a and b are angles)

sin(a)+sin(b) = 2sin([a+b]/2)cos([a+b]/2)

cos(a)+cos(b) = 2cos([a+b]/2)cos([a-b]/2)

cos(a)-cos(b) = -2sin([a+b]/2)sin([a-b]/2)

Half, Double, and Triple Angle formulas (SQRT(arg) means take the square root of arg)

~ Half Angle

sin(Θ/2) = SQRT([1-cos(Θ)]/2)

cos(Θ/2) = SQRT([1+cos(Θ)]/2)

tan(Θ/2) = sin(Θ)/[1+cos(Θ)] = [1-cos(Θ)]/sin(Θ)

~Double Angle

sin(2Θ)=2sin(Θ)cos(Θ) = 2tan(Θ)/[1+tan2(Θ)]

cos(2Θ)=cos2(Θ)-sin2(Θ) = 2cos2(Θ) – 1 = 1-2sin2(Θ) = [1-tan2(Θ)]/[1+tan2(Θ)]

tan(2Θ)=2tan(Θ)/[1-tan2(Θ)]

~Triple Angle

sin(3Θ) = 3sin(Θ)-4sin3(Θ)

cos(3Θ) = 4cos3(Θ) – 3cos(Θ)

tan(3Θ) = [3tan(Θ) – tan3(Θ)]/[1-3tan2(Θ)]

This post is part of the series: Trig Help

Everything you need to know to get through your trig class. Whether in high school or college, the tips, tricks, formulas and methods you need can all be found here.

• A Guide to Proving Trig Identities
• Ace the Trig Exam With This Study Guide
• Functions List for Trigonometry

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5 Ways to Deal with Trigonometry Homework Assignments

Trigonometry homework assignments can be tricky. Students often complain that they don’t have enough time to deal with all the homework. Even those who have strong math skills often need some help in order to get everything done on time. If you realize that you don’t know what to do, you can consult your teacher, ask your friends to help you, or follow great guidelines on how to deal with trigonometry problems effectively.

It’s a good idea to use one of the options provided below:

• Study your class notes carefully.

You’ll be able to deal with trigonometry assignments if you learn and understand all the material given by your teacher. Usually, your homework tasks are similar to tasks you’ve solved in class, so it makes sense to look through your class notes before you start to work on your homework. If you don’t have all the notes, you should ask your classmates to share theirs.

• Watch a trigonometry study video.

Most students agree that educational how-to videos are very helpful. Since there’re many high-quality video lessons related to different trigonometry topics on the Web, you can easily find something useful. Typically, these lessons are short but informative, so you won’t waste time studying something that you actually don’t need. Don’t hesitate to ask around in order to find out where your classmates watch these videos.

• Use online calculators.

All the students use calculators while working on math assignments. However, online calculators provide more functions that are useful. This software allows students to calculate what they need, along with plotting the results and getting step-by-step explanations. This option is very helpful when you want to learn what steps to take in order to solve your assignments and check the answers you got.

• Consider hiring an online tutor.

This option is useful for those students who have poor math skills and want to catch up with the material. An experienced professional will help you solve the assigned problems, explain what you have to do in order to deal with similar assignments, and tell you where to find high-quality educational sources. You can find both free and paid online tutoring services.

• Go to a math study center.

Many schools have math study centers designed to help students deal with their algebra and trigonometry homework. There, you’ll find plenty of different resources, including textbooks, how-to manuals, collections of great tips and tricks, sample problems, answers to typical homework problems, and more. A center’s instructor will recommend right resources for you.

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Test prep and homework help from private online Trigonometry tutors

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Top 355 online Trigonometry tutors

12 years of tutoring

Deoli , India

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Lakshmi Narain College of Technology

Professional Mathematics tutor with 12+ years of international experience/AP Calculus AB and BC/GCSE/Calculus I and II/Algebra/Trigonometry/Geometry/Pre-Calculus

Welcome to my profile! 😊 I'm an engineering graduate with tons of experience in online tutoring worldwide. 🌍 I've had the pleasure of delivering thousands of successful lessons. With 12 years of experience in tutoring students from diverse backgrounds, I have developed a deep understanding of various math subjects, including algebra, geometry, calculus, trigonometry, and more. My goal is to make math enjoyable and accessible by breaking down complex concepts into simpler, relatable terms. 🎯 I believe that anyone can succeed in math with the right guidance, patience, and practice. 😊✨ As an online tutor, I utilize the latest technological tools and interactive resources to create an engaging learning environment. 🖥️Through clear explanations, step-by-step problem-solving strategies, and interactive exercises, I empower my students to build a strong foundation and develop critical thinking skills. 📚🧩 I am committed to providing a supportive and encouraging learning experience. I believe in fostering a positive and open-minded atmosphere where students feel comfortable asking questions, exploring concepts, and making mistakes. I am patient, flexible, and adaptable to different learning styles, ensuring that each session is tailored to suit your unique strengths and weaknesses. 🤗💪 Whether you need help with homework assignments, exam preparation, or simply want to deepen your understanding of math, I am here to guide you on your mathematical journey. Let's work together to boost your confidence, improve your grades, and unlock your full potential in math! 🚀📈🔢 Contact me today to schedule a session, and let's embark on an exciting mathematical adventure together. 😄🎉

Subjects : AP Calculus AB/BC, Algebra, Algebra 1, Algebra 2, Calculus, Elementary Math, Geometry, Math/Science, Maths, Pre-Algebra, Pre-Calculus, SAT II Mathematics Level 1, SAT II Mathematics Level 2, SAT Mathematics, Trigonometry

10 years of tutoring

English , Urdu

Hyderabad , India

USD $ 10 /hr

Osmania University , Sri Krishna Devaraya University

Online Math teacher over 10 years of experience

Hello! I'm Arif. I am an experienced Mathematics tutor and have more than 10 years experience in tutoring various topics be it related to grade 5 to 10 of Cambridge, UK, IB and American curriculum. 1.Arithmetic 2.Algebra 3.Trigonometry 4.Geometry 5. Statistics 6.Probability and many more... to a wide range of students from scratch. I also teach for competitive level exams . I'm a Gold topper in my bachelor's for academics. I love teaching math to students and with my unique methods, I make my students solve complex calculations in seconds without the use of calculator. With my experience in clearing several competitive exams and National level exams, I can help you in getting perfect scores in all competitive exams of GCSE, IGCSE, GRE, GED, SAT, IB, CBSE etc. Thank you. Have a nice and joyful day!

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Vancouver , Canada

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University of British Columbia

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I have got my PhD in Electrical and Computer Engineering from UBC. I have 14+ years of tutoring and teaching experience in high schools, colleges, and universities. I was serving as a faculty member at Electrical Engineering Department of one of the Tehran's universities for 5 years. I have published more than 25 papers in different journals and conferences. For more details, please find my Google Scholar profile. Some of the subjects I teach/tutor for K-12, college, and university students are as follows: > Electric Circuits > Data Science > Machine Learning > Python > Coding > Algorithms > Physics > College/University Math courses (first year and second year) > Math 7, 8, 9, 10 > Pre-Calculus 11, 12 > IB (HL, SL) Math, Stat and Physics > AP Calculus AB & BC > AP Statistics > Advanced Calculus, Calculus I, II > Algebra > Probability and Statistics > Trigonometry and Geometry > Discrete Mathematics > SSAT (Math) Exam prep: lower level (for grades 4 and 5), middle level (for grades 6, 7, 8), and upper level (for grades 8, 9, 10, 11) > GRE (Quantitative) Exam Prep

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23 years of tutoring

Punjabi , English , Hindi

Patiala , India

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Navpreet B.

Punjabi University Patiala. India

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I have been teaching Mathematics at all levels for the last 23 years. I have a Ph.D. in Topology. and I teach at a University in India. I have also helped and tutored students from Primary to Secondary Schools. Deeply interested in teaching and discussing Mathematics with young school students at their level, as they are our future. I offer 15 minutes free interactive session to all my potential students, to get to know their expectations to enable me to meaningfully assist them in gaining excellent mathematical understanding and skill.

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20 years of tutoring

Nairobi , Kenya

USD $ 25 /hr

Mathematics, Physics and chemistry. 20+ yrs teaching experience .

With my 20+ years experience in teaching,my students have been able to achieve high success rates in their grades and final exams. I assist students who need help in the following areas: Homework and assignment help. Remedial tutoring. Exam preperation( Common Enteance, Checkpoint, I GCSE, A level cambridge and edexcel, IB DP SL $ HL, AP and SATS . My students can have access to a wide range of resources like Worksheets, pdf books, work books and past exam papers. Continuous evaluation and monitoring of my students' progress is my priority .

Subjects : A-Levels, AP Calculus AB/BC, AP Chemistry, AP Physics, Algebra, Chemistry, Elementary Math, Functions, IB, IGCSE, Mathematics, Physics

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- A ferris wheel with a radius of 25 meters makes one rotation every 36 seconds. At the bottom of the ride, the passenger is 1 meter above the ground. - Let h be the height, above ground, of a passenger. Determine h as a function of time if h = 51 meter at t = 0. - Find the height h after 45 seconds. - Linda measures the angle of elevation from a point on the ground to the top of the tree and find it to be 35o. She then walks 20 meters towards the tree and finds the angle of elevation from this new point to the top of the tree to be 45o. Find the height of the tree. (Round answer to three significant digits) - Prove that [cos(x) - sin(x)][cos(2x) - sin(2x)] = cos(x) - sin(3x) - Find the exact value of [ tan(25º) + tan(50º)] / [ 1 - tan(25º) tan(50º] - What is the angle B of triangle ABC, given that A = 46º, b = 4 and c = 8?(Note: side a faces angle A, side b faces angle B and side c faces angle C). - Write an equation for a sine function with an amplitude of 5/3 , a period of π/2, and a vertical shift of 4 units up.

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Trigonometry is a field of mathematics that studies the connection between various triangular angles and other angles. It investigates the connections between different angles as well as their uses. The most common terminologies in trigonometry include cosecant (cosec), secant (sec), cotangent (cot), tangent (tan), cosine (cos), and sine (sin). Learning such unfamiliar terms and the need to calculate more triangles and double angles than you had anticipated may make it challenging to understand trigonometry fully. Our math experts strive to assist with thorough explanations since they know math’s importance and difficulty. Therefore, don’t worry, no matter what assignment problems appear on your worksheets for trigonometry. Our online trigonometry homework help will increase your likelihood of better academic performance, particularly in this area of mathematics.

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Trigonometry causes a lot of problems for students. It is considered one of the most severe branches of math. What are sine and cosine? What are tangent and cotangent? What is a numerical circle? When a teacher asks these harmless questions, students turn pale and try to divert the conversation in the other direction. However, these are simple concepts. Moreover, trigonometry is no more difficult than other disciplines. You just need to clearly understand the answers to these questions from the very beginning. It is very important. If you want to understand trigonometry better, you need to ask us, “help me with my trigonometry homework,” and we will gladly assist you with any task.

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