156k views
1 vote
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.

User Ubreddy
by
7.5k points

1 Answer

7 votes

Answer::


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

Step-by-step 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}}=-(2)/(3) \end{gathered}

User Enchance
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories