Question

If sin θ=.55 what is the value of cos θ and explain why

Answer 1

`cos(\theta)=(+/-)0.84`

Explanation:

we know that

`sin^2(\theta)+cos^2(\theta)=1` ----> by trigonometric identity

we have

`sin(\theta)=0.55`

substitute

`(0.55)^2+cos^2(\theta)=1`

`cos^2(\theta)=1-(0.55)^2`

`cos^2(\theta)=0.6975`

`cos(\theta)=(+/-)√(0.6975)`

`cos(\theta)=(+/-)0.84`

Remember that

If the sine of angle theta is positive, then the angle theta lie on the I Quadrant or II Quadrant

therefore

If the angle theta is on the I Quadrant the cosine will be positive

If the angle theta is on the II Quadrant the cosine will be negative