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:

$\cot \theta=\frac{\cos\theta}{\sin\theta}=\frac{\frac{adjacent}{hypothenuse}}{\frac{opposite}{hypothenuse}}=\frac{adjacent}{opposite}$

We also have that:

$cot^{-1}\theta=\frac{\pi}{2}-\tan ^{-1}\theta$

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

$\theta=\cot ^{-1}(\cot \theta)=\cot ^{-1}(\frac{20}{21})=\frac{\pi}{2}-\tan ^{-1}(\frac{20}{21})$

So,

$\theta\approx-42.032$

Then, we have:

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

and

$\sin \theta=\sin (\frac{\pi}{2}-\tan ^{-1}(\frac{20}{21}))=-0.67$