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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.

Respuesta :

LammettHash
I think you mean to say [tex]\cos^2\theta=\dfrac14[/tex]. If [tex]\theta[/tex] is in the third quadrant, then [tex]\sin\theta<0[/tex] and [tex]\cos\theta<0[/tex]. Recall that


[tex]\sin^2\theta+\cos^2\theta=1\implies\sin\theta=\pm\sqrt{1-\cos^2\theta}[/tex]

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

[tex]\sin\theta=-\sqrt{1-\dfrac14}=-\dfrac{\sqrt3}2[/tex]

We also know to expect [tex]\cos\theta<0[/tex], so

[tex]\cos\theta=\pm\sqrt{\dfrac14}\implies\cos\theta=-\dfrac12[/tex]


By definition, we have

[tex]\cot\theta=\dfrac{\cos\theta}{\sin\theta}[/tex]

and so

[tex]\cot\theta=\dfrac{-\frac12}{-\frac{\sqrt3}2}=\dfrac1{\sqrt3}[/tex]
Iilyevans

Answer:

1. cot⁡θ is 1/3.

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

Step-by-step 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

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