Question

If θ is an angle in standard position and its terminal side passes through the point (-3,2). Find the exact values for sin, cosine, and tangent.

Answer 1

Answer::

$\sin \theta=\frac{2}{\sqrt[]{13}},\cos \theta=-\frac{3}{\sqrt[]{13}},\tan \theta=-\frac{2}{3}$

Explanation:

If the terminal side passes through the point (-3,2), then the angle is in Quadrant II.

• Adjacent Side, x=-3

,

• Opposite Side, y=2

Next, we find the hypotenuse, r:

$\begin{gathered} r^2=(-3)^2+2^2 \\ r^2=9+4 \\ r^2=13 \\ r=\sqrt[]{13} \end{gathered}$

Thus, the exact values of the trig ratios are:

$\begin{gathered} \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{2}{\sqrt[]{13}} \\ \cos \theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=-\frac{3}{\sqrt[]{13}} \\ \tan \theta=\frac{\text{Opposite}}{\text{Adjacent}}=-\frac{2}{3} \end{gathered}$