Textbook Question
Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (3 , ―4)
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 2, Problem 28
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.
29.6° , 49.7°
Verified step by step guidance1
Recall that the sum of the interior angles of any triangle is always 180 degrees. This is a fundamental property of triangles.
Identify the given angles: the first angle is 29.6° and the second angle is 49.7°.
Set up an equation to find the third angle, which we can call \( x \):
\[ 29.6 + 49.7 + x = 180 \]
Combine the known angles on the left side:
\[ 79.3 + x = 180 \]
Solve for \( x \) by subtracting 79.3 from both sides:
\[ x = 180 - 79.3 \]
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triangle Angle Sum Property
The sum of the interior angles of any triangle is always 180 degrees. This fundamental property allows us to find the measure of an unknown angle when the other two angles are known by subtracting their sum from 180°.
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Sum and Difference of Tangent
Basic Arithmetic Operations
Solving for the unknown angle requires simple arithmetic, specifically addition and subtraction. Adding the two given angles and subtracting their sum from 180° yields the measure of the third angle.
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04:12Algebraic Operations on Vectors
Angle Measurement Units
Angles are measured in degrees (°), a unit that divides a full rotation into 360 parts. Understanding this unit is essential for interpreting the given angle measures and performing calculations accurately.
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5:31Reference Angles on the Unit Circle
Related Practice
Textbook Question
Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (―8 , 15)
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Find the measure of each marked angle. See Example 2.
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