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Question 12 of 18

beginning of content:

M:N:MC:11

Tags:
SAT

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This question contributes to the total Math Test score but does not contribute to a subscore within the Math Test.
Additional Topics in Math

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Which of the following is equal to sin open parentheses straight pi over 5 close parentheses?

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minus cos open parentheses straight pi over 5 close parentheses

Correct Answer: 
No

minus sin open parentheses straight pi over 5 close parentheses

Correct Answer: 
No

cos open parentheses fraction numerator 3 straight pi over denominator 10 end fraction close parentheses

Correct Answer: 
Yes

sin open parentheses fraction numerator 7 straight pi over denominator 10 end fraction close parentheses

Correct Answer: 
No

View Correct Answer

Choice C is correct. Sine and cosine are related by the equation: sin open parentheses x close parentheses equals cos open parentheses straight pi over 2 minus x close parentheses. Therefore, sin open parentheses straight pi over 5 close parentheses equals cos open parentheses straight pi over 2 minus straight pi over 5 close parentheses comma which reduces to cos open parentheses fraction numerator 3 straight pi over denominator 10 end fraction close parentheses.

Choice A is not the correct answer. This answer may result from a misunderstanding about trigonometric relationships. A student may think that cosine is the opposite function of sine, and therefore think that the negative of the cosine of an angle is equivalent to the sine of that angle.

Choice B is not the correct answer. This answer may result from a misunderstanding of the unit circle and how it relates to trigonometric expressions. A student may think that, on a coordinate grid, the negative sign only changes the orientation of the triangle formed, not the value of the trigonometric expression.

Choice D is not the correct answer. The student mistakenly remembers the relationship between sine and cosine and adds straight pi over 2 to the angle measure instead of subtracting the angle measure from straight pi over 2.

Question Difficulty: 
hard
Objective: 

Students must understand radian measure and have a conceptual understanding of trigonometric relationships.