7. Write the exact answer for cos() sin() 8. Write the exact answer for cos( + cos (7)
7. Write the exact answer for cos() sin() 8. Write the exact answer for cos( + cos (7)
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°.
Related questions
Question
Please anwser numbers 7 and 8! Thank you!
![**Trigonometric Identities and Formulas**
This section contains practice problems related to trigonometric identities and formulas. For the exercises involving the given triangle, use the below details:
**Problem 6:**
Use the triangle illustrated to find the trigonometric values:
- \(\sin(2\beta)\)
- \(\cos(2\beta)\)
- \(\sin\left(\dfrac{\pi}{2}\right)\)
- \(\cos\left(\dfrac{\pi}{2}\right)\)
*Note: The triangle is a right triangle where the hypotenuse is 25, the base adjacent to angle \(\beta\) is 24, and the opposite side to angle \(\beta\) is unknown; however, you can calculate it using the Pythagorean theorem if needed.*
**Problem 7:**
Write the exact answer for:
\[
\cos\left(\dfrac{\pi}{3}\right) \sin\left(\dfrac{\pi}{4}\right)
\]
**Problem 8:**
Write the exact answer for:
\[
\cos\left(\dfrac{5\pi}{12}\right) + \cos\left(\dfrac{7\pi}{12}\right)
\]
**Diagram Explanation:**
- The diagram displays a right triangle.
- The hypotenuse is labeled as 25.
- The base (adjacent to angle \(\beta\)) is labeled as 24.
- The angle at the base adjacent to the 24 unit side is labeled as \(\beta\).
- The angle opposite to the base of 24 units and adjacent to the hypotenuse is labeled as \(\alpha\).
Use the properties of the right triangle and trigonometric formulas to solve the given problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f80e2b9-2cfd-4c3a-b29d-7104fd1276e9%2F24fd287a-a067-42ec-8525-542355bd0acb%2Fwo9po7h_processed.png&w=3840&q=75)
Transcribed Image Text:**Trigonometric Identities and Formulas**
This section contains practice problems related to trigonometric identities and formulas. For the exercises involving the given triangle, use the below details:
**Problem 6:**
Use the triangle illustrated to find the trigonometric values:
- \(\sin(2\beta)\)
- \(\cos(2\beta)\)
- \(\sin\left(\dfrac{\pi}{2}\right)\)
- \(\cos\left(\dfrac{\pi}{2}\right)\)
*Note: The triangle is a right triangle where the hypotenuse is 25, the base adjacent to angle \(\beta\) is 24, and the opposite side to angle \(\beta\) is unknown; however, you can calculate it using the Pythagorean theorem if needed.*
**Problem 7:**
Write the exact answer for:
\[
\cos\left(\dfrac{\pi}{3}\right) \sin\left(\dfrac{\pi}{4}\right)
\]
**Problem 8:**
Write the exact answer for:
\[
\cos\left(\dfrac{5\pi}{12}\right) + \cos\left(\dfrac{7\pi}{12}\right)
\]
**Diagram Explanation:**
- The diagram displays a right triangle.
- The hypotenuse is labeled as 25.
- The base (adjacent to angle \(\beta\)) is labeled as 24.
- The angle at the base adjacent to the 24 unit side is labeled as \(\beta\).
- The angle opposite to the base of 24 units and adjacent to the hypotenuse is labeled as \(\alpha\).
Use the properties of the right triangle and trigonometric formulas to solve the given problems.
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