Question

If Sin θ = 12/13, then what is the value of Cot θ?

A) 13/12 B) 5/13 C) 5/12 D) 13/5

Answer 1

Step-by-step explanation:

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Answer 2

Answer

The correct option is C) 5/12

The value of cotθ is 5/12

Given

• sinθ = 12/13

To Find

• The value of cotθ

Solution

We have ,

$\sf \implies \sin \theta = \dfrac{12}{13}$

We know that

$\sf \implies \sin^2\theta+\cos^2\theta = 1 \\\\ \sf\implies (\dfrac{12}{13})^2 + \cos^2\theta = 1 \\\\ \sf\implies \cos^2\theta = 1-\dfrac{144}{169} \\\\ \sf\implies \cos^2\theta = \dfrac{169-144}{169} \\\\ \sf\implies \cos^2\theta = \dfrac{25}{169} \\\\ \sf\implies \cos\theta = \dfrac{5}{13}$

Now we are given to find cotθ

$\sf \therefore \cot \theta = \dfrac{\cos\theta}{\sin\theta} \\\\ \sf \implies \cot \theta = \dfrac{\dfrac{5}{13}}{\dfrac{12}{13}} \\\\ \sf\implies \cot\theta=\dfrac{5}{12}$