Question

Find the values of the trigonometric functions from the given informationGiven cot θ=20/21 and sin θ<0, fine cos θ and sin θ

Answer 1

The cotangent of an angle is equal to:

`\cot \theta=(\cos\theta)/(\sin\theta)=((adjacent)/(hypothenuse))/((opposite)/(hypothenuse))=(adjacent)/(opposite)`

We also have that:

`cot^(-1)\theta=(\pi)/(2)-\tan ^(-1)\theta`

Now, we can find the angle θ using the cotangent inverse formula:

`\theta=\cot ^(-1)(\cot \theta)=\cot ^(-1)((20)/(21))=(\pi)/(2)-\tan ^(-1)((20)/(21))`

So,

`\theta\approx-42.032`

Then, we have:

`\cos \theta=\cos ((\pi)/(2)-\tan ^(-1)((20)/(21)))=\text{ 0.74}`

and

`\sin \theta=\sin ((\pi)/(2)-\tan ^(-1)((20)/(21)))=-0.67`