Angles and the Trigonometric Functions

Trigonometric Functions graphs, Inverse Trigonometric Functions

Trigonometric Identities and Equations

Laws of Sines, Cosines and Vectors

Complex Numbers, Polar Coordinates and Parametric Equations

A Way to remember the Entire Unit Circle for Trigonometry

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/3c2d66a4c5d891ee-1684265404224.jpg" alt="" />

tan 0

Domain and Range of Sine and Cosine

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 3𝜋, 𝜋, 5𝜋, 3𝜋, 7𝜋, and 2𝜋.
4 2 4 4 2 4 

a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.
b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/4c055c40951448ab-1684150027118.jpg" alt="" />

cot 15𝜋/2

Deriving Trig Ratios for 45 degrees (pi/4 radians)

How to remember the unit circle 

Examples with Trigonometric Functions: Even, Odd or Neither, Example 2

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 3𝜋, 𝜋, 5𝜋, 3𝜋, 7𝜋, and 2𝜋.
4 2 4 4 2 4 

a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.
b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/69b1b78796edb37b-1684150204472.jpg" alt="" />

cos 9𝜋/2

In Exercises 19–24, 
a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric function.
b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

cos (-𝜋/6)<img src="https://lightcat-files.s3.amazonaws.com/problem_images/a2957aafa9f20d15-1684266175277.jpg" alt="" />

Determine 6 Trig Function Values Using The Unit Circle (Radians)

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 3𝜋, 𝜋, 5𝜋, 3𝜋, 7𝜋, and 2𝜋.
4 2 4 4 2 4 

a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.
b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/44d3c2ca19dff7f6-1684150851743.jpg" alt="" />

sin 11𝜋/4

Domain and Range of Trigonometric Functions - Part 1

Finding Values of Trigonometric Functions with the Unit Circle

Find Six Trig Function Values Using Reference Triangles - Mult. of pi/4

Using Periodic Properties of Trigonometric Functions

Cos 3pi/4

Even, Odd or Neither, Trigonometric Functions, Example 4

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/004542a1554bd2c4-1684265904779.jpg" alt="" />

In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
cos 3𝜋/2

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/398d596207607326-1684265329586.jpg" alt="" />

cos 2𝜋/3

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/c02c615118940441-1684265676192.jpg" alt="" />

In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
sec 5𝜋/3

Even and Odd Trig Functions

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/f064e656b39a7aa9-1684265501859.jpg" alt="" />

In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
csc 4𝜋/3

Examples with Trigonometric Functions: Even, Odd or Neither, Example 1

How To Evaluate Trigonometric Functions Using Periodic Properties

Periodic Properties - Example 1

A Trick to Remember Values on The Unit Circle

Deriving Values on the Unit Circle

Learn how to find the sine of 5 pi over 4 without a calculator

Use the Unit Circle to Find the Indicated Value

Periodic properties of the trigonometric functions

Examples with Trigonometric Functions: Even, Odd or Neither, Example 3

Domain, Range, and Signs of Trigonometric Function

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/094aed265b3e882b-1684265998668.jpg" alt="" />

In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
tan 3𝜋/2

Evaluating for all six trig functions for a point on the unit circle

How to evaluate tangent, cotangent, secant and cosecant functions

Even and odd properties of trig functions

In Exercises 19–24, 
a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric function.
b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

tan 5𝜋/3<img src="https://lightcat-files.s3.amazonaws.com/problem_images/fb36df9d5035956c-1684266701476.jpg" alt="" />

Sine & Cosine of π/4

What are even and odd trigonometric functions

Understanding Even Odd Identities

How to find the range of the sine and cosine graph

In Exercises 19–24, 
a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric function.
b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

tan (-11𝜋/6)<img src="https://lightcat-files.s3.amazonaws.com/problem_images/436a7c27f7f65ae9-1684266891725.jpg" alt="" />

What is the domain of sine and cosine graph

trigonometry - Periodic Properties 

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 3𝜋, 𝜋, 5𝜋, 3𝜋, 7𝜋, and 2𝜋.
4 2 4 4 2 4 

a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.
b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/1aa52149c4a2d27d-1684150070833.jpg" alt="" />

tan 𝜋

In Exercises 19–24, 
a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric function.
b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

cos 𝜋/3<img src="https://lightcat-files.s3.amazonaws.com/problem_images/c1f905711bbbac2a-1684266353275.jpg" alt="" />

In Exercises 19–24, 
a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric function.
b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

sin 5𝜋/6<img src="https://lightcat-files.s3.amazonaws.com/problem_images/71d661ef52d8fe2a-1684266536525.jpg" alt="" />

Find the Exact Values of the Trigonometric Functions at &pi; / 4

Trigonometric Functions: The Unit Circle

This course covers topics including trigonometric functions (with graphs and inverse functions), identities and equations, solutions of triangles, complex numbers and more.

College Trigonometry

https://static.studychannel.pearsonprd.tech/courses/trigonometry/thumbnails/trigonometry

#FFFFFF

Keeley Ridner

The Organic Chemistry Tutor

Kelsey Huelsman

Mathispower4u

Professor Heather Pierce

Mario's Math Tutoring

Marty Brandl

 Rafael Gavilan-Castro

Don't Memorise

Brian McLogan

OneClass

Math and Stats Help

slcmath@pc

Krista King

The Infinite Looper

Matthew Brown

MathAfterMath

patrickJMT

Use the Definitions of Trigonometric Functions of Any Angle

Use the Signs of the Trigonometric Functions

Find Reference Angles

Use Reference Angles to Evaluate Trigonometric Functions

Trigonometric Functions of Any Angle

Recognize and Use the Vocabulary of Angles

Use Degree Measure

Use Radian Measure

Convert Between Degrees and Radians

Draw Angles in Standard Position

Find Coterminal Angles

Find the Length of a Circular Arc

Find the area of a sector

Use Linear and Angular Speed to Describe Motion on a Circular Path

Introduction to Trigonometry

Angles and Radian Measure

Use a Unit Circle to Define Trigonometric Functions of Real Numbers

Recognize the Domain and Range of Sine and Cosine Functions

Use Even and Odd Trigonometric Functions

Use Periodic Properties

Use Right Triangles to Evaluate Trigonometric Functions

Find Function Values for 30&deg;(&pi; / 6), 45&deg;(&pi; / 4), and 60&deg;(&pi; / 3)

Recognize and Use Fundamental Identities

Use Equal Cofunctions of Complements

Evaluate Trigonometric Functions With a Calculator

Use Right Triangle Trigonometry to Solve Applied Problems

Right Triangle Trigonometry

General Chemistry

Jules

Classification of Matter (1)

Classification of Matter (2)

Classification of Matter - Example

Study the key concepts of Physics with descriptive videos, questions, and more

Physics

Patrick

Introduction to Units & the SI System

Metric Prefixes

Scientific Notation

General Biology

Jason

Introduction to Biology

Unicellular vs. Multicellular

Characteristics of Life

Financial Accounting

Brian

Dive deep into Psychology with videos, practice problems, and more.

Psychology

Microeconomics

The first in a two-course sequence introduces the basic structure and functions of the human body

Anatomy & Physiology

Bruce

College Algebra covers algebraic topics and skills necessary to succeed in college-level math

College Algebra

Organic Chemistry

Johnny

Genetics

Kylia

GOB Chemistry

Dive deep into General, Organic, and Biological Chemistry with videos, practice problems, and more.

Intro to Chemistry

Microbiology

Cell Biology

Analytical Chemistry

Study topics incliding trogonometric functions, identities and equations, solutions of triangles, complex numbers, and other topics as time permits

Trigonometry

Learn the toughest concepts covered in Precalculus with step-by-step video tutorials and practice problems by world-class tutors

Precalculus

Biochemistry

Macroeconomics

My Channels

College Channels

Skills Channels

Professional Channels

Chemistry

Biology

Math

Business

Social Sciences

Michelle Barry Franco

Building Great Presentations

Eric Zackrison, PhD

Critical Thinking And Problem Solving

Sam Bennett

Embracing Times Of Uncertainty

Nicole Tetreault, PhD

Emotional Intelligence Basics

Eugene Choi, PharmD

Enhancing Your Critical Thinking Skills

Jason Richardson, PsyD

Habits To Win Every Day

Alyssa Lowery, PhD

Having Powerful Advanced Conversations

Don Gilman, EdD

How To Influence & Persuade

Amy Matthews

Leadership Skills For Rising Stars

Listening To Lead

Michael Shermer, PhD

Making Decisions Under Uncertainty

Lynne Hurdle

Mistakes To Avoid When Resolving Conflict

Michael Veltri

Overcoming Decision Making Traps

Mike Vardy

Prioritizing Effectively

Secrets Of Effective Prioritization

Strategies To Build Up Your Creativity

Tools For Decision Making

Tutti Taygerly

Unleash And Advance Your Creativity

Winning Collaboration: How To Work More Effectively With Different Personalities