Trigonometry Examples

$\frac{\sin (c)}{\sin (119.7)} = \frac{\sin (30.2)}{\sin (3.3)}$

Step 1

Simplify $\frac{\sin (c)}{\sin (119.7)}$ .

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Step 1.1

Rewrite $\frac{\sin (c)}{\sin (119.7)}$ as a product.

$\sin (c) \frac{1}{\sin (119.7)} = \frac{\sin (30.2)}{\sin (3.3)}$

Step 1.2

Write $\sin (c)$ as a fraction with denominator $1$ .

$\frac{\sin (c)}{1} \cdot \frac{1}{\sin (119.7)} = \frac{\sin (30.2)}{\sin (3.3)}$

Step 1.3

Simplify.

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Step 1.3.1

Divide $\sin (c)$ by $1$ .

$\sin (c) \frac{1}{\sin (119.7)} = \frac{\sin (30.2)}{\sin (3.3)}$

Step 1.3.2

Convert from $\frac{1}{\sin (119.7)}$ to $\csc (119.7)$ .

$\sin (c) \csc (119.7) = \frac{\sin (30.2)}{\sin (3.3)}$

Step 2

Simplify $\frac{\sin (30.2)}{\sin (3.3)}$ .

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Step 2.1

Rewrite $\frac{\sin (30.2)}{\sin (3.3)}$ as a product.

$\sin (c) \csc (119.7) = \sin (30.2) \frac{1}{\sin (3.3)}$

Step 2.2

Write $\sin (30.2)$ as a fraction with denominator $1$ .

$\sin (c) \csc (119.7) = \frac{\sin (30.2)}{1} \cdot \frac{1}{\sin (3.3)}$

Step 2.3

Simplify.

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Step 2.3.1

Divide $\sin (30.2)$ by $1$ .

$\sin (c) \csc (119.7) = \sin (30.2) \frac{1}{\sin (3.3)}$

Step 2.3.2

Convert from $\frac{1}{\sin (3.3)}$ to $\csc (3.3)$ .

$\sin (c) \csc (119.7) = \sin (30.2) \csc (3.3)$

Step 3

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

No solution

Step 4