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

Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set o

Korolek [52]

Answer:

Step-by-step explanation:

10(10m+6)<=12

100m+60<=12 Distributive Property

100m <=12-60

100m <=-48

m <=-48/100

m <=-.48

This says values for m that are less than or equal to -.48

-.48 is between -1 and 0 so the answer is B

6 0

3 years ago

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Using the slope formula, find the slope of the line through the given points.

UNO [17]

Answer:

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

= (-5--5)/ (9--8)

= (-5+5)/(9+8)

= 0/17

The slope it 0

This is a horizontal line because the y value doesn't change. If the y value doesn't change, the slope it zero.

4 0

2 years ago

Parker spends 1/4 of his earnings on rent and 1/6 of his earnings on entertainment

mote1985 [20]

Answer:

Cool

Step-by-step explanation:

3 0

2 years ago

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