5|8 If sin 0=- (a) cos 0 0 in quadrant II, find the exact value of (b) sin 0+ π (c) cos 8- SH (b) sin 0+. T (c) cos 0-- 3 (0+ 47) (a) cos 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (d) tan 0+ π 6 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
5|8 If sin 0=- (a) cos 0 0 in quadrant II, find the exact value of (b) sin 0+ π (c) cos 8- SH (b) sin 0+. T (c) cos 0-- 3 (0+ 47) (a) cos 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (d) tan 0+ π 6 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 6GP
Related questions
Question
![### Trigonometric Function Evaluation
Given that \( \sin \theta = \frac{5}{8} \) and \( \theta \) is in quadrant II, find the exact values of the following trigonometric expressions:
#### (a) \( \cos \theta \)
\[ \cos \theta = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
#### (b) \( \sin \left( \theta + \frac{\pi}{6} \right) \)
\[ \sin \left( \theta + \frac{\pi}{6} \right) = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
#### (c) \( \cos \left( \theta - \frac{\pi}{3} \right) \)
\[ \cos \left( \theta - \frac{\pi}{3} \right) = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
#### (d) \( \tan \left( \theta + \frac{\pi}{4} \right) \)
\[ \tan \left( \theta + \frac{\pi}{4} \right) = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F812a333f-5569-4734-822a-5aed0505f779%2F891a0220-b563-4ade-91a7-bf7afa0a71c4%2Ffcwfjbk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometric Function Evaluation
Given that \( \sin \theta = \frac{5}{8} \) and \( \theta \) is in quadrant II, find the exact values of the following trigonometric expressions:
#### (a) \( \cos \theta \)
\[ \cos \theta = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
#### (b) \( \sin \left( \theta + \frac{\pi}{6} \right) \)
\[ \sin \left( \theta + \frac{\pi}{6} \right) = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
#### (c) \( \cos \left( \theta - \frac{\pi}{3} \right) \)
\[ \cos \left( \theta - \frac{\pi}{3} \right) = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
#### (d) \( \tan \left( \theta + \frac{\pi}{4} \right) \)
\[ \tan \left( \theta + \frac{\pi}{4} \right) = \_\_\_ \]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
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