Question

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.

Answer 1

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

Answer 2

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}`