Trigonometry Examples

$\cos (\frac{13 π}{15}) \cos (- \frac{π}{5}) - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$

Step 1

Evaluate $\cos (\frac{13 π}{15})$ .

$- 0.91354545 \cos (- \frac{π}{5}) - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$

Step 2

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$- 0.91354545 \cos (\frac{9 π}{5}) - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$

Step 3

Evaluate $\cos (\frac{9 π}{5})$ .

$- 0.91354545 \cdot 0.80901699 - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$

Step 4

Multiply $- 0.91354545$ by $0.80901699$ .

$- 0.7390738 - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$

Step 5

Evaluate $\sin (\frac{13 π}{15})$ .

$- 0.7390738 - 1 \cdot 0.40673664 \sin (- \frac{π}{5})$

Step 6

Multiply $- 1$ by $0.40673664$ .

$- 0.7390738 - 0.40673664 \sin (- \frac{π}{5})$

Step 7

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$- 0.7390738 - 0.40673664 \sin (\frac{9 π}{5})$

Step 8

Evaluate $\sin (\frac{9 π}{5})$ .

$- 0.7390738 - 0.40673664 \cdot - 0.58778525$

Step 9

Multiply $- 0.40673664$ by $- 0.58778525$ .

$- 0.7390738 + 0.2390738$

Step 10

Add $- 0.7390738$ and $0.2390738$ .

$- 0.5$