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=(adjacent)/(hypotenuse)=(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}}=(4)/(5)`

Therefore, sinθ = 4/5

Finally,