Table of contents

0. Review of College Algebra4h 45m

Rationalizing Denominators
17m

Pythagorean Theorem & Basics of Triangles
17m

Basics of Graphing
30m

Functions
41m

Transformations
45m

Asymptotes
4m

Solving Linear Equations
31m

Solving Quadratic Equations
55m

Complex Numbers
41m

1. Measuring Angles40m

Angles in Standard Position
12m

Coterminal Angles
8m

Complementary and Supplementary Angles
10m

Radians
8m

2. Trigonometric Functions on Right Triangles2h 5m

Trigonometric Functions on Right Triangles
45m

Special Right Triangles
30m

Cofunctions of Complementary Angles
26m

Solving Right Triangles
23m

3. Unit Circle1h 19m

Defining the Unit Circle
14m

Trigonometric Functions on the Unit Circle
9m

Common Values of Sine, Cosine, & Tangent
11m

Reference Angles
38m

Reciprocal Trigonometric Functions on the Unit Circle
6m

4. Graphing Trigonometric Functions1h 19m

Graphs of the Sine and Cosine Functions
32m

Phase Shifts
14m

Graphs of Secant and Cosecant Functions
10m

Graphs of Tangent and Cotangent Functions
21m

5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m

Inverse Sine, Cosine, & Tangent
28m

Evaluate Composite Trig Functions
44m

Linear Trigonometric Equations
28m

6. Trigonometric Identities and More Equations2h 34m

Introduction to Trigonometric Identities
1h 4m

Sum and Difference Identities
1h 3m

Double Angle Identities
16m

Solving Trigonometric Equations Using Identities
9m

7. Non-Right Triangles1h 38m

Law of Sines
49m

Law of Cosines
30m

Area of SAS & ASA Triangles
19m

8. Vectors2h 25m

Geometric Vectors
28m

Vectors in Component Form
32m

Direction of a Vector
23m

Unit Vectors and i & j Notation
27m

Dot Product
22m

Cross Product
11m

9. Polar Equations2h 5m

Polar Coordinate System
29m

Convert Points Between Polar and Rectangular Coordinates
26m

Convert Equations Between Polar and Rectangular Forms
29m

Graphing Other Common Polar Equations
39m

10. Parametric Equations1h 6m

Graphing Parametric Equations
12m

Eliminate the Parameter
32m

Writing Parametric Equations
21m

11. Graphing Complex Numbers1h 7m

Graphing Complex Numbers
6m

Polar Form of Complex Numbers
22m

Products and Quotients of Complex Numbers
14m

Powers of Complex Numbers (DeMoivre's Theorem)
23m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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1:48 minutes

Problem 100

Textbook Question

Give two positive and two negative angles that are coterminal with the given quadrantal angle. 270°

Verified step by step guidance

Understand that coterminal angles differ by full rotations of 360°. This means if you add or subtract multiples of 360° to the given angle, you get coterminal angles.

Start with the given angle, which is 270°, a quadrantal angle lying on the negative y-axis.

To find two positive coterminal angles, add 360° and 720° to 270° respectively, using the formula \(\theta + 360^\circ \times n\) where \(n\) is a positive integer.

To find two negative coterminal angles, subtract 360° and 720° from 270° respectively, using the formula \(\theta - 360^\circ \times n\) where \(n\) is a positive integer.

List the resulting angles as your two positive and two negative coterminal angles with 270°.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. To find coterminal angles, you add or subtract multiples of 360° from the given angle. This concept helps identify angles that have the same trigonometric values.

Quadrantal Angles

Quadrantal angles are angles whose terminal sides lie along the x-axis or y-axis, typically at 0°, 90°, 180°, 270°, or 360°. These angles are important because their trigonometric values are often simple or undefined, and they serve as reference points in the coordinate plane.

Positive and Negative Angles

Positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise. Understanding this distinction is essential when finding coterminal angles, as you can add or subtract 360° to generate both positive and negative coterminal angles.

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Master Example 1 with a bite sized video explanation from Patrick

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Textbook Question

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 541°

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Textbook Question

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 1000°

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Textbook Question

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 8440°

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Textbook Question

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. -5280°

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Textbook Question

Write an expression that generates all angles coterminal with each angle. Let n represent any integer. ―90°

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Textbook Question

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 174 °