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0. Fundamental Concepts of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

Pythagorean Theorem & Basics of Triangles
(0)

1. Equations and Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions & Graphs(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential and Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Measuring Angles(0)

Angles in Standard Position
(0)

Coterminal Angles
(0)

Complementary and Supplementary Angles
(0)

Radians
(0)

8. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
(0)

Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

9. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
(0)

Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

10. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

11. Inverse Trigonometric Functions and Basic Trig Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

12. Trigonometric Identities (0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

13. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

14. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

15. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

16. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

17. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

18. Systems of Equations and Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

19. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

20. Sequences, Series & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

21. Combinatorics and Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

22. Limits & Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

23. Intro to Derivatives & Area Under the Curve(0)

Tangent Lines & Derivatives
(0)

Limits at Infinity
(0)

Limits of Sequences
(0)

Area Under a Curve
(0)

9. Unit Circle

Trigonometric Functions on the Unit Circle

9. Unit Circle

Trigonometric Functions on the Unit Circle: Videos & Practice Problems

Video Lessons Practice Worksheet

20 problems

Problem 1Multiple Choice

Determine the exact value of the given function.

sin (-5π/3)

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Problem 2Multiple Choice

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using even and odd properties of trigonometric functions.

Unit circle showing coordinates for trigonometric functions at specific angles.

a. cos(4π/3)

b. cos(-4π/3)

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Problem 3Multiple Choice

Determine the exact values of sin p, cos p, and tan p where p = -7π.

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Problem 4Multiple Choice

Determine the six circular function values of θ. The angle θ is in standard position and the terminal side intersects the unit circle at the specified point.

Unit circle showing angle θ with coordinates (-12/37, -35/37) for trigonometric functions.

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Problem 5Multiple Choice

Considering the interval [0, 2π), find the exact values of p.

sin p = -1/2

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Problem 6Multiple Choice

Considering the interval [0, π/2], find the approximate value of x. Round the answer to four decimal places.

cos x = 0.7816

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Problem 7Multiple Choice

Considering the interval [0, π/2], find the approximate value of x. Round the answer to four decimal places.

cot x = 0.6837

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Problem 8Multiple Choice

Determine the exact value of the given function.

tan (5π/6)

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Problem 9Multiple Choice

Determine the exact value of the given function.

csc (-7π/4)

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Problem 10Multiple Choice

What is the x-coordinate of the point on the unit circle corresponding to an angle of 0 degrees?

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Problem 11Multiple Choice

If the coordinates of a point on the unit circle are (1/2, √3/2), what is the sine of the corresponding angle?

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Problem 12Multiple Choice

Using the alphabetical order mnemonic, determine the cosine of an angle if its coordinates on the unit circle are (-√2/2, √2/2).

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Problem 13Multiple Choice

Calculate the tangent of an angle with coordinates (1/2, √3/2) on the unit circle.

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Problem 14Multiple Choice

What is the tangent of 90 degrees?

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Problem 15Multiple Choice

For an angle in the third quadrant with coordinates (-3/5, -4/5), what are the signs of sine, cosine, and tangent?

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Problem 16Multiple Choice

Find the tangent of an angle with coordinates (-3/5, -4/5) on the unit circle.

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Problem 17Multiple Choice

What is the tangent of 60 degrees?

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Problem 18Multiple Choice

Why is it acceptable for the sine of an angle in the third quadrant to be negative?

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Problem 19Multiple Choice

If an angle in the second quadrant has coordinates (-√3/2, 1/2), what is the tangent of this angle?

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Problem 20Multiple Choice

What is the y-coordinate of the point on the unit circle corresponding to an angle of 90 degrees?

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Defining the Unit Circle Practice Problems Common Values of Sine, Cosine, & Tangent Practice Problems

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Trigonometric Functions on the Unit Circle: Videos & Practice Problems

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