We have been given that $\text{sin}(A)=\frac{12}{13}$ and angle A is in quadrant 1. We are asked to find the exact value of $\text{cot}(A)$ in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

$\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}$

Now we will find adjacent side using Pythagoras theorem as:

$\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2$

$\text{Adjacent}^2=13^2-12^2$

$\text{Adjacent}^2=169-144$

$\text{Adjacent}^2=25$

Let us take positive square root on both sides:

$\sqrt{\text{Adjacent}^2}=\sqrt{25}$

$\text{Adjacent}=5$

Therefore, adjacent side of angle A is 5 units.

$\text{cot}(A)=\frac{5}{12}$

Therefore, the exact value of cot A is $\frac{5}{12}$ .

5 0

2 years ago

Pleaseeeee help im horrible at math

Murljashka [212]

Answer:

The Answer is gonna be D. 2

This is the right Answer:3

I hope you are having a great day ❤️❤️❤️

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2 years ago

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Explain what step is incorrect pls help quick!?!??

AlekseyPX

Answer:

Step 1 (IM AM NOT SURE NOT MY FAULT IF ITS WRONG)

Step-by-step explanation:

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3 years ago

If there's a 9% tax, and the couch is $227.49 what will the total be?

ZanzabumX [31]

Answer

Step-by-step explanation:

227.49 x 1.09 = 247.96

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2 years ago

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