Textbook Question
In Exercises 1–60, verify each identity.sin x sec x = tan x
Ch. 3 - Trigonometric Identities and Equations
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 3, Problem 3.3.51
In Exercises 47–54, use the figures to find the exact value of each trigonometric function. cos(α/2)
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Identify the given angle \( \alpha \) and the trigonometric function you need to find, which in this case is \( \cos \alpha \).
Recall the definition of cosine in a right triangle: \( \cos \alpha = \frac{\text{adjacent side}}{\text{hypotenuse}} \).
Examine the figure provided (usually a right triangle) to determine the lengths of the adjacent side and the hypotenuse relative to angle \( \alpha \).
Substitute the lengths of the adjacent side and hypotenuse into the cosine ratio formula: \( \cos \alpha = \frac{\text{adjacent}}{\text{hypotenuse}} \).
Simplify the fraction if possible to find the exact value of \( \cos \alpha \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Functions
Trigonometric functions like sine, cosine, and tangent relate the angles of a right triangle to the ratios of its sides. Understanding these functions is essential for finding exact values based on given angles or side lengths.
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Introduction to Trigonometric Functions
Unit Circle and Angle Measures
The unit circle represents angles and their corresponding trigonometric values on a circle of radius one. Knowing how to interpret angles in radians or degrees on the unit circle helps in determining exact trigonometric values.
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06:11Introduction to the Unit Circle
Reference Angles and Quadrants
Reference angles are acute angles used to find trigonometric values for angles in different quadrants. Recognizing the quadrant of the angle helps determine the sign (positive or negative) of the trigonometric function.
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5:31Reference Angles on the Unit Circle
Related Practice
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In Exercises 1–6, use the figures to find the exact value of each trigonometric function.cos 2θ
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Textbook Question
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sin 2θ
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