Question

cos eand sin e< 0. Identify the quadrant of the terminal side of O andfind sin e.

Answer 1

We are given that cosθ = 3/5

Recall from trigonometric ratios,

$\cos \theta=\frac{adjacent}{hypotenuse}=\frac{3}{5}$

Let us apply the Pythagorean theorem to find the third side

$\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a^2=5^2-3^2 \\ a^2=25-9 \\ a^2=16 \\ a^{}=\sqrt[]{16} \\ a=4 \end{gathered}$

So, the opposite side is 4

Recall from trigonometric ratios,

$\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{4}{5}$

Therefore, sinθ = 4/5

Finally,