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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

Find the values of the trigonometric functions from the given informationGiven cot-example-1
User Bmalicoat
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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

User Isagalaev
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