Question

Find the value of the trig function indicated.

Answer 1

In the given triangle, we have

`\tan(\theta) = (20)/(15) = \frac43`

Recall that

`\sin^2(\theta) + \cos^2(\theta) = 1 \implies \tan^2(\theta) + 1 = \sec^2(\theta)`

Solving for
`\sec(\theta)`, we have

`\sec(\theta) = √(\tan^2(\theta) + 1) = √(\left(\frac43\right)^2 + 1) = \sqrt{\frac{25}9} = \boxed{\frac53}`

(D)