Ch. 1 - Trigonometric Functions

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 1 - Trigonometric Functions

Problem 13

Chapter 2, Problem 13

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 45°

Verified step by step guidance

Understand the definitions: The complement of an angle is what, when added to the angle, equals 90°. The supplement of an angle is what, when added to the angle, equals 180°.

To find the complement of the given angle (45°), set up the equation: \(\text{complement} + 45^\circ = 90^\circ\).

Solve for the complement by subtracting 45° from both sides: \(\text{complement} = 90^\circ - 45^\circ\).

To find the supplement of the given angle (45°), set up the equation: \(\text{supplement} + 45^\circ = 180^\circ\).

Solve for the supplement by subtracting 45° from both sides: \(\text{supplement} = 180^\circ - 45^\circ\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. To find the complement of a given angle, subtract the angle's measure from 90°. For example, the complement of 45° is 90° - 45° = 45°.

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. To find the supplement of a given angle, subtract the angle's measure from 180°. For example, the supplement of 45° is 180° - 45° = 135°.

Angle Measurement and Units

Angles are measured in degrees, representing the amount of rotation between two rays. Understanding how to manipulate and interpret these measurements is essential for solving problems involving complements and supplements.

Recommended video:

5:31

Reference Angles on the Unit Circle

Related Practice

Textbook Question

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. csc θ , given that sin θ = ―3/7

Textbook Question

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Textbook Question

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―8 , 15)

views

Textbook Question

Find the measure of each marked angle.

Textbook Question

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

<IMAGE>

views

Textbook Question

Find the measure of each marked angle.

views