Question

Hey I know nothing and this is my final exam

Answer 1

First, let's look at the trigonometric ratios;

`\sin \Theta=(opposite)/(hypotenuse)`
`\cos \Theta=(adjacent)/(hypoteunse)`
`\tan \Theta=(opposite)/(adjacent)`

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

A.

`\sec \Theta=(1)/(\cos \Theta)`
`=\frac{1}{\frac{adjacent}{\text{hypotenuse}}}`
`=\frac{hypotenuse}{\text{adjacent}}`

option A is not true

B

`\csc \Theta=(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=(hypotenuse)/(adjacent)`

D

`\cot \Theta=(1)/(\tan \Theta)`
`=\frac{1}{\frac{opposite}{\text{adjacent}}}`
`=\frac{adjacent}{\text{opposite}}`

option D is not true

Hence, only option C is true