CPM Homework Help : PC3 Problem 10-87

If $\sin(x) = −\frac { 3 } { 7 }$ , $π ≤ x ≤ \frac { 3 \pi } { 2 }$ , calculate exact values for $\sin(2x)$ and $\cos(2x)$ .

Step:

Draw and label a circle with the reference angle in the correct quadrant.
Calculate the length of the unlabeled side.

Formulas:

Double - Angle Formula: Sine
$\sin(2α) = 2\sin(α)\cos(α)$

Double - Angle Formulas: Cosine
1. $\cos(2α) = 1 − 2\sin^2(α)$
2. $\cos2(α) = 2\cos2(α) − 1$
3. $\cos(2α) = \cos^2(α) − \sin^2(α)$

Circle with right triangle in third quadrant, radius as hypotenuse, labeled 7, vertical leg labeled negative 3.