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Question

If sinθ+cosθ=0 and 0<θ<π, then θ is equal to


A

0

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B

π4

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C

π2

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D

3π4

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Solution

The correct option is D

3π4


Solve the given function for θ:

From the given equation, we can conclude that

sinθ=-cosθ

Divide both the sides by cosθ,

sinθcosθ=-cosθcosθtanθ=-1

With the given condition 0<θ<π, we know that tan is negative in the second quadrant.

Then, the only viable angle is 3π4.

Hence, the correct option is (D).


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