Trigonometry Examples

$\sin (- \frac{3}{5} - \frac{5}{13})$

Step 1

Use the sum formula for sine to simplify the expression. The formula states that $\sin (A + B) = \sin (A) \cos (B) + \cos (A) \sin (B)$ .

$\sin (- \frac{3}{5}) \cos (\frac{5}{13}) + \cos (- \frac{3}{5}) \sin (\frac{5}{13})$

Step 2

Remove parentheses.

$\sin (- \frac{3}{5}) \cos (\frac{5}{13}) + \cos (- \frac{3}{5}) \sin (\frac{5}{13})$

Step 3

Simplify each term.

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Step 3.1

Evaluate $\sin (- \frac{3}{5})$ .

$- 0.56464247 \cos (\frac{5}{13}) + \cos (- \frac{3}{5}) \sin (\frac{5}{13})$

Step 3.2

Evaluate $\cos (\frac{5}{13})$ .

$- 0.56464247 \cdot 0.9269428 + \cos (- \frac{3}{5}) \sin (\frac{5}{13})$

Step 3.3

Multiply $- 0.56464247$ by $0.9269428$ .

$- 0.52339128 + \cos (- \frac{3}{5}) \sin (\frac{5}{13})$

Step 3.4

Evaluate $\cos (- \frac{3}{5})$ .

$- 0.52339128 + 0.82533561 \sin (\frac{5}{13})$

Step 3.5

Evaluate $\sin (\frac{5}{13})$ .

$- 0.52339128 + 0.82533561 \cdot 0.37520264$

Step 3.6

Multiply $0.82533561$ by $0.37520264$ .

$- 0.52339128 + 0.3096681$

Step 4

Add $- 0.52339128$ and $0.3096681$ .

$- 0.21372317$