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Θ is in Quadrant III and cos^2 0= 1/4

A. Evaluate cotθ.

B. In two or more sentences, explain how to find the value of cotθ.

2 Answers

3 votes

Answer:

1. cot⁡θ is 1/3.

2. Find tan by dividing sin/cos then inverse the answer.

Explanation:

to do this, you need to understand:

inverse trig functions

pythagoream theorem (to find the missing value in sin which was opp)

Study you guys! I know this might sound annoying but trig really isn't as hard as it looks. I recommend The Organic Chem Tutor on youtu

User NomeN
by
8.0k points
3 votes
I think you mean to say
\cos^2\theta=\frac14. If
\theta is in the third quadrant, then
\sin\theta<0 and
\cos\theta<0. Recall that



\sin^2\theta+\cos^2\theta=1\implies\sin\theta=\pm√(1-\cos^2\theta)

We expect
\sin\theta to be negative, so we take the negative root. We end up with


\sin\theta=-√(1-\frac14)=-\frac{\sqrt3}2

We also know to expect
\cos\theta<0, so


\cos\theta=\pm√(\frac14)\implies\cos\theta=-\frac12


By definition, we have


\cot\theta=(\cos\theta)/(\sin\theta)

and so


\cot\theta=\frac{-\frac12}{-\frac{\sqrt3}2}=\frac1{\sqrt3}
User Mamut
by
7.8k points

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