If \sin(\theta)=-\frac{1}{4}\sin and \theta is in the 3rd quadrant,

chillywilly12a

chillywilly12a

Answered question

2021-09-06

If sin(θ)=14sin and θ is in the 3rd quadrant, find cos(θ)

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2021-09-07Added 94 answers

Given:
sinθ=14 and θ lies in 3rd quadrant.
To find the value of cosθ
Since we have the trigonometric identity,
sin2θ+cos2θ=1
(14)2+cos2θ=1
cos2θ=1116
cos2θ=1516
cosθ=1516
cosθ=±154
cosθ=154
θ is in 3rd quadrant and sinθ and cosθ are negative in 3rd quadrant
Hence cosθ=154

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