Question

What is the correct answer for all? I need help!!

Answer 1

1) We have to find csc(theta).

The csc of an angle can be written as:

$\csc (\theta)=\frac{1}{\sin (\theta)}=\frac{hypotenuse}{opposite}$

Here, the hypotenuse is 8*sqrt(2) and the opposite side has a length of 8, so we can write:

$\csc (\theta)=\frac{8\sqrt[]{2}}{8}=\sqrt[]{2}$

Answer: B) sqrt(2)

2) The cot can be written as:

$\cot (\theta)=\frac{1}{\tan (\theta)}=\frac{\text{adyacent}}{\text{opposite}}$

In this case, with adyacent of length 15 and opposite of length 8, we have:

$\cot (\theta)=\frac{15}{8}$

Answer: D) 15/8

3)

$\sin (\theta)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{20}{25}=\frac{4}{5}$

Answer: C) 4/5

4)

$\sin (\theta)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5}$

Answer: C) 3/5

5)

$\csc (\theta)=\frac{\text{hypotenuse}}{\text{opposite}}=\frac{15}{9}=\frac{5}{3}$

Answer: A) 5/3