Trigonometry Examples

$\cos (\frac{3}{5} - \frac{4}{5})$

Step 1

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

$\cos (\frac{3}{5}) \cdot \cos (\frac{4}{5}) + \sin (\frac{3}{5}) \cdot \sin (\frac{4}{5})$

Step 2

Remove parentheses.

$\cos (\frac{3}{5}) \cdot \cos (\frac{4}{5}) + \sin (\frac{3}{5}) \cdot \sin (\frac{4}{5})$

Step 3

Simplify each term.

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Step 3.1

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

$0.82533561 \cdot \cos (\frac{4}{5}) + \sin (\frac{3}{5}) \cdot \sin (\frac{4}{5})$

Step 3.2

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

$0.82533561 \cdot 0.6967067 + \sin (\frac{3}{5}) \cdot \sin (\frac{4}{5})$

Step 3.3

Multiply $0.82533561$ by $0.6967067$ .

$0.57501686 + \sin (\frac{3}{5}) \cdot \sin (\frac{4}{5})$

Step 3.4

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

$0.57501686 + 0.56464247 \cdot \sin (\frac{4}{5})$

Step 3.5

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

$0.57501686 + 0.56464247 \cdot 0.71735609$

Step 3.6

Multiply $0.56464247$ by $0.71735609$ .

$0.57501686 + 0.40504971$

Step 4

Add $0.57501686$ and $0.40504971$ .

$0.98006657$