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Q.

If sin⁡θ=12 and cos⁡θ=−32,  then the general value of θ is (n∈Z)

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a

2nπ+5π6

b

2nπ+π6

c

2nπ+7π6

d

2nπ+π4

answer is A.

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Detailed Solution

sin⁡θ=1/2 and cos⁡θ=−3/2⇒ θ lies in the second quadrant. ⇒ sin⁡θ=sin⁡5π/6;cos⁡θ=cos⁡5π/6;∴ θ=2nπ+(5π/6),n∈Z
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If sin⁡θ=12 and cos⁡θ=−32,  then the general value of θ is (n∈Z)