Precalculus Examples

$\sin (\frac{11 π}{14} - \frac{11 π}{60})$

Step 1

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

$\sin (\frac{11 π}{14}) \cos (\frac{11 π}{60}) - \cos (\frac{11 π}{14}) \sin (\frac{11 π}{60})$

Step 2

Remove parentheses.

$\sin (\frac{11 π}{14}) \cos (\frac{11 π}{60}) - \cos (\frac{11 π}{14}) \sin (\frac{11 π}{60})$

Step 3

Simplify each term.

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Step 3.1

Evaluate $\sin (\frac{11 π}{14})$ .

$0.6234898 \cos (\frac{11 π}{60}) - \cos (\frac{11 π}{14}) \sin (\frac{11 π}{60})$

Step 3.2

Evaluate $\cos (\frac{11 π}{60})$ .

$0.6234898 \cdot 0.83867056 - \cos (\frac{11 π}{14}) \sin (\frac{11 π}{60})$

Step 3.3

Multiply $0.6234898$ by $0.83867056$ .

$0.52290254 - \cos (\frac{11 π}{14}) \sin (\frac{11 π}{60})$

Step 3.4

Evaluate $\cos (\frac{11 π}{14})$ .

$0.52290254 - - 0.78183148 \sin (\frac{11 π}{60})$

Step 3.5

Multiply $- 1$ by $- 0.78183148$ .

$0.52290254 + 0.78183148 \sin (\frac{11 π}{60})$

Step 3.6

Evaluate $\sin (\frac{11 π}{60})$ .

$0.52290254 + 0.78183148 \cdot 0.54463903$

Step 3.7

Multiply $0.78183148$ by $0.54463903$ .

$0.52290254 + 0.42581594$

Step 4

Add $0.52290254$ and $0.42581594$ .

$0.94871849$