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Subject Test Math 2

Question 13 of 28

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SAT Subject Test

If  sin space function application theta equals 0.57, then sin function application left parenthesis pi minus theta right parenthesis equals

Select an Answer

negative 0.57

Correct Answer: 
No

negative 0.43

Correct Answer: 
No

0

Correct Answer: 
No

0.43

Correct Answer: 
No

0.57

Correct Answer: 
Yes

The correct answer is E.

One way to determine the value of sin function application left parenthesis pi minus theta right parenthesis is to apply the sine of difference of two angles identity: sin function application left parenthesis pi minus theta right parenthesis equals sin space function application pi invisible times space cos space function application theta minus cos space function application pi space invisible times sin space function application theta. Since sin space function application pi equals 0 and cos function application pi equals negative 1, the identity gives sin function application left parenthesis pi minus theta right parenthesis equals 0 left parenthesis cos space function application theta right parenthesis minus left parenthesis negative 1 right parenthesis left parenthesis sin space function application theta right parenthesis equals sin space function application theta. Therefore, sin function application left parenthesis pi minus theta right parenthesis equals 0.57.

Another way to determine the value of sin function application left parenthesis pi minus theta right parenthesis is to apply the supplementary angle trigonometric identity for the sine: sin function application left parenthesis pi minus theta right parenthesis equals sin space function application theta. Therefore, sin function application left parenthesis pi minus theta right parenthesis equals 0.57.

Question Difficulty: 
medium