Trigonometry Examples

$\sin (\frac{4}{5} + \frac{5}{13})$

Step 1

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

$\sin (\frac{4}{5}) \cos (\frac{5}{13}) + \cos (\frac{4}{5}) \sin (\frac{5}{13})$

Step 2

Remove parentheses.

$\sin (\frac{4}{5}) \cos (\frac{5}{13}) + \cos (\frac{4}{5}) \sin (\frac{5}{13})$

Step 3

Simplify each term.

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Step 3.1

Evaluate $\sin (\frac{4}{5})$ .

$0.71735609 \cos (\frac{5}{13}) + \cos (\frac{4}{5}) \sin (\frac{5}{13})$

Step 3.2

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

$0.71735609 \cdot 0.9269428 + \cos (\frac{4}{5}) \sin (\frac{5}{13})$

Step 3.3

Multiply $0.71735609$ by $0.9269428$ .

$0.66494807 + \cos (\frac{4}{5}) \sin (\frac{5}{13})$

Step 3.4

Evaluate $\cos (\frac{4}{5})$ .

$0.66494807 + 0.6967067 \sin (\frac{5}{13})$

Step 3.5

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

$0.66494807 + 0.6967067 \cdot 0.37520264$

Step 3.6

Multiply $0.6967067$ by $0.37520264$ .

$0.66494807 + 0.2614062$

Step 4

Add $0.66494807$ and $0.2614062$ .

$0.92635427$