Trigonometry Examples

$\sin (B) = 12 (\frac{\sin (42)}{22})$

Step 1

Simplify $12 (\frac{\sin (42)}{22})$ .

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Step 1.1

Evaluate $\sin (42)$ .

$\sin (B) = 12 (\frac{0.6691306}{22})$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $12$ .

$\sin (B) = 2 (6) \frac{0.6691306}{22}$

Step 1.2.2

Factor $2$ out of $22$ .

$\sin (B) = 2 \cdot 6 \frac{0.6691306}{2 \cdot 11}$

Step 1.2.3

Cancel the common factor.

$\sin (B) = 2 \cdot 6 \frac{0.6691306}{2 \cdot 11}$

Step 1.2.4

Rewrite the expression.

$\sin (B) = 6 (\frac{0.6691306}{11})$

Step 1.3

Combine $6$ and $\frac{0.6691306}{11}$ .

$\sin (B) = \frac{6 \cdot 0.6691306}{11}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Multiply $6$ by $0.6691306$ .

$\sin (B) = \frac{4.01478363}{11}$

Step 1.4.2

Divide $4.01478363$ by $11$ .

$\sin (B) = 0.36498033$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$B \approx 3.66510003 + 2 π n, 5.75967793 + 2 π n$ , for any integer $n$

Step 3