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Question

For any acute angle θ select the trigonometric functions with a positive value.

A
sec(7π2+θ)
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B
cos(5π2θ)
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C
cosec(5π2+θ)
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D
sin(3π2θ)
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Solution

The correct option is C cosec(5π2+θ)
Given an acute angle θ and we have to find which of the following trigonometric functions have a positive value.

a.sin(3π2θ)
3π2θ corresponds to angle in the third quadrant where both sin and cos are negative.
sin(3π2θ)=cosθ
Hence, it's value will be negative.

b.cos(5π2θ)
5π2θ corresponds to an angle in the first quadrant where all trigonomettric functions are positive.
cos(5π2θ)=+sinθ
Hence, it's value will be positive.

c.sec(7π2+θ)
7π2+θ corresponds to angle in the fourth qudrant where sec of an angle is positive..
sec(7π2+θ)=cosec θ
Hence, it's value will be positive.

c.cosec (5π2+θ)
5π2+θ corresponds to angle in the second qudrant where cosec of an angle is positive.
cosec (7π2+θ)=secθ
Hence, it's value will be positive.

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