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If cosθ=1/√2, where θ is an acute angle, then find the value of sinθ. - Geometry

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If `cosθ=1/sqrt(2)`, where θ is an acute angle, then find the value of sinθ.

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Solution

`cosθ=1/sqrt(2)`

`cos^2theta=(1/sqrt2)^2=1/2`

`cos^2theta+ sin^2theta=1`

`1/2+sin^2theta=1`

`sin^2theta=1-1/2=1/2`

`sintheta=sqrt(1/2)=1/sqrt2`

 

Concept: Trigonometric Ratios of Complementary Angles
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