Question

If sin theta=1/2 and cos theta=-root3/2, then the general value of theta is

A) 2n(pi)+5pi/6; n belongs to I
B) 2n(pi)+pi/6; n belongs to I
C) 2n(pi)+7pi/6; n belongs to I
D) 2n(pi)+pi/4; n belongs to I

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Answer 1

Answer:

tari sasu ne hat daje samji gayo

Answer 2

Given :  Sinθ = 1/2 ,  Cosθ = √3 / 2

To Find :   general value of theta θ

Solution:

Sinθ = 1/2

Sin π /6 = 1/2

θ = nπ + (-1)ⁿ( π /6)    n belongs to Integer

Cosθ = √3 / 2

Cos π /6 = √3 / 2

θ = 2nπ ± π /6    n belongs to Integer

θ = nπ + (-1)ⁿ( π /6)

make it  2 nπ    as cos have  2nπ ± π /6

=> θ = 2 nπ + ( π /6)

Hence common is   2 nπ + ( π /6)

θ =  2n(π)+π /6; n belongs to Integer  

Another way cos and sin both together are positive in 1st Quadrant Only

Hence θ =  2nπ + π /6 ; n belongs to Integer  

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