Question

If cos(θ)=2853 with θin Q IV, what is sin(θ)?

Answer 1

Answer:
`\sin \theta=(-45)/(53)`

Explanation:

Since we have given that

`\cos\theta=(28)/(53)`

And we know that θ is in the Fourth Quadrant.

So, Except cosθ and sec θ, all trigonometric ratios will be negative.

As we know the "Trigonometric Identity":

`\cos^2\theta+\sin^2\theta=1\\\\\sin \theta=√(1-\cos^2\theta)\\\\\sin \theta=\sqrt{1-((28)/(53))^2}=\sqrt{(53^2-28^2)/(53^2)}\\\\\sin \theta=\sqrt{(2025)/(53^2)}\\\\\sin \theta=(45)/(53)`

It must be negative due to its presence in Fourth quadrant.

Hence,
`\sin \theta=(-45)/(53)`