Question

Check all that apply. If cose = 15, then :

Answer 1

Given:

$cos\theta=\frac{15}{17}$

Required:

To check the given option.

Explanation:

Use the trigonometric ratio formula.

$cos\theta=\frac{adjacent}{hypotenuse}=\frac{15}{17}$

Thus adjacent = 15

hypotenuse = 17

Now by using the pythoguras theorem we will find the opposite side.

$\begin{gathered} opp.=\sqrt{(hyp.)^2-(adj.)^2} \\ opp.=\sqrt{(17)^2-(15)^2} \\ opp.=\sqrt{289-225} \\ opp.=\sqrt{64} \\ opp.=8 \end{gathered}$

Now we will check the given options.

First, we will check option (A).

$\begin{gathered} sec\theta=\frac{hyp.}{adj.} \\ sec\theta=\frac{17}{15} \end{gathered}$

option A is correct.

Now we will check option (B).

$\begin{gathered} csc\theta=\frac{hyp.}{opp.} \\ csc\theta=\frac{17}{8} \end{gathered}$

option (B) is incorrect.

Now we will check option (C).

$\begin{gathered} tan\theta=\frac{opp.}{adj.} \\ tan\theta=\frac{8}{15} \end{gathered}$

option (C) is correct.

Now we will check option (D).

$\begin{gathered} sin\theta=\frac{opp.}{hyp.} \\ sin\theta=\frac{8}{17} \end{gathered}$

option (D) is incorrect.

Final answer:

option (A) and (C) is the correct answer.