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13. Find the exact value of sin 157.5° and cos 157.5° and tan157.5⁰ Leave answers exact and simplified (no decimals).

13. Find the exact value of sin 157.5° and cos 157.5° and tan157.5⁰ Leave answers exact and simplified (no decimals).

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Trigonometric Function Value Calculation - Educational Exercise** --- **Question 13:** **Objective:** Determine the exact values of trigonometric functions for a given angle. Specifically, calculate the exact values for \( \sin 157.5^\circ \), \( \cos 157.5^\circ \), and \( \tan 157.5^\circ \). Ensure that answers are exact and simplified (do not use decimals). **Instructions:** 1. Find the exact value of \( \sin 157.5^\circ \). 2. Find the exact value of \( \cos 157.5^\circ \). 3. Find the exact value of \( \tan 157.5^\circ \). Leave all answers in exact, simplified form without using decimals. --- **Explanation:** To solve these, one would typically use known angle sum or difference identities, half-angle identities, or appropriate trigonometric transformations. \( 157.5^\circ \) can be expressed as \( 180^\circ - 22.5^\circ \), which may help in using certain trigonometric identities efficiently. The detailed simplification process includes algebraic manipulations to maintain the exact form without converting to decimal approximations. **Note to students:** When solving such problems, make sure to reference your trigonometric identities section and ensure the answers remain in their simplest exact form.
Transcribed Image Text:**Trigonometric Function Value Calculation - Educational Exercise** --- **Question 13:** **Objective:** Determine the exact values of trigonometric functions for a given angle. Specifically, calculate the exact values for \( \sin 157.5^\circ \), \( \cos 157.5^\circ \), and \( \tan 157.5^\circ \). Ensure that answers are exact and simplified (do not use decimals). **Instructions:** 1. Find the exact value of \( \sin 157.5^\circ \). 2. Find the exact value of \( \cos 157.5^\circ \). 3. Find the exact value of \( \tan 157.5^\circ \). Leave all answers in exact, simplified form without using decimals. --- **Explanation:** To solve these, one would typically use known angle sum or difference identities, half-angle identities, or appropriate trigonometric transformations. \( 157.5^\circ \) can be expressed as \( 180^\circ - 22.5^\circ \), which may help in using certain trigonometric identities efficiently. The detailed simplification process includes algebraic manipulations to maintain the exact form without converting to decimal approximations. **Note to students:** When solving such problems, make sure to reference your trigonometric identities section and ensure the answers remain in their simplest exact form.
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