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Use the sum-to-product identities to rewrite the expression. sin 18° + sin 10° Which expression is equal to sin 18° + sin 10°? O A. -2 sin 14° sin 4° O B. 2 cos 14° sin 4° O C. 2 sin 14° cos 4° D. 2 cos 14° cos 4°

Use the sum-to-product identities to rewrite the expression. sin 18° + sin 10° Which expression is equal to sin 18° + sin 10°? O A. -2 sin 14° sin 4° O B. 2 cos 14° sin 4° O C. 2 sin 14° cos 4° D. 2 cos 14° cos 4°

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Using Sum-to-Product Identities Use the sum-to-product identities to rewrite the expression: \[ \sin 18^\circ + \sin 10^\circ \] ### Question Which expression is equal to \( \sin 18^\circ + \sin 10^\circ \)? - A. \(-2 \sin 14^\circ \sin 4^\circ\) - B. \(2 \cos 14^\circ \sin 4^\circ\) - C. \(2 \sin 14^\circ \cos 4^\circ\) - D. \(2 \cos 14^\circ \cos 4^\circ\) Click to select your answer. [Button: Save for Later] ### Explanation This question asks you to use the sum-to-product identities to simplify the given trigonometric expression. Sum-to-product identities are trigonometric identities that express sums of sines or cosines as products of sines and cosines. The relevant identities are: \[ \sin a + \sin b = 2 \sin \left(\frac{a+b}{2}\right) \cos \left(\frac{a-b}{2}\right) \] Here, if we let \( a = 18^\circ \) and \( b = 10^\circ \), the expression \( \sin 18^\circ + \sin 10^\circ \) can be rewritten as follows: \[ \sin 18^\circ + \sin 10^\circ = 2 \sin \left(\frac{18^\circ + 10^\circ}{2}\right) \cos \left(\frac{18^\circ - 10^\circ}{2}\right) \] \[ = 2 \sin \left(\frac{28^\circ}{2}\right) \cos \left(\frac{8^\circ}{2}\right) \] \[ = 2 \sin 14^\circ \cos 4^\circ \] Therefore, the correct answer is option C: ### Correct Answer: C. \(2 \sin 14^\circ \cos 4^\circ\)
Transcribed Image Text:### Using Sum-to-Product Identities Use the sum-to-product identities to rewrite the expression: \[ \sin 18^\circ + \sin 10^\circ \] ### Question Which expression is equal to \( \sin 18^\circ + \sin 10^\circ \)? - A. \(-2 \sin 14^\circ \sin 4^\circ\) - B. \(2 \cos 14^\circ \sin 4^\circ\) - C. \(2 \sin 14^\circ \cos 4^\circ\) - D. \(2 \cos 14^\circ \cos 4^\circ\) Click to select your answer. [Button: Save for Later] ### Explanation This question asks you to use the sum-to-product identities to simplify the given trigonometric expression. Sum-to-product identities are trigonometric identities that express sums of sines or cosines as products of sines and cosines. The relevant identities are: \[ \sin a + \sin b = 2 \sin \left(\frac{a+b}{2}\right) \cos \left(\frac{a-b}{2}\right) \] Here, if we let \( a = 18^\circ \) and \( b = 10^\circ \), the expression \( \sin 18^\circ + \sin 10^\circ \) can be rewritten as follows: \[ \sin 18^\circ + \sin 10^\circ = 2 \sin \left(\frac{18^\circ + 10^\circ}{2}\right) \cos \left(\frac{18^\circ - 10^\circ}{2}\right) \] \[ = 2 \sin \left(\frac{28^\circ}{2}\right) \cos \left(\frac{8^\circ}{2}\right) \] \[ = 2 \sin 14^\circ \cos 4^\circ \] Therefore, the correct answer is option C: ### Correct Answer: C. \(2 \sin 14^\circ \cos 4^\circ\)
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