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

List the steps to calculate the slope/rate of change using a calculator.

andrezito [222]

Is this what you’re talking about

4 0

2 years ago

|2x-5|=9 please awnser i need this for math

7nadin3 [17]

Answer:

Step-by-step explanation

2x = 14

divide by 2

8 0

1 year ago