Question

hey I know nothing and this is my final exam

Answer 1

First, let's look at the trigonometric ratios;

$\sin \Theta=\frac{opposite}{hypotenuse}$$\cos \Theta=\frac{adjacent}{hypoteunse}$$\tan \Theta=\frac{opposite}{adjacent}$

Let's check each option and see if it is true

A.

$\sec \Theta=\frac{1}{\cos \Theta}$$=\frac{1}{\frac{adjacent}{\text{hypotenuse}}}$$=\frac{hypotenuse}{\text{adjacent}}$

option A is not true

B

$\csc \Theta=\frac{1}{\sin \Theta}$$=\frac{1}{\frac{opposite}{\text{hypotenuse}}}$$=\frac{hypotenuse}{\text{opposite}}$

option B is also not true

Option C is correct because

$\sec \Theta=\frac{hypotenuse}{adjacent}$

D

$\cot \Theta=\frac{1}{\tan \Theta}$$=\frac{1}{\frac{opposite}{\text{adjacent}}}$$=\frac{adjacent}{\text{opposite}}$

option D is not true

Hence, only option C is true