Trigonometry Examples

$\frac{c}{c^{2}} = \frac{\sin (x)}{\sin (x^{2})}$

Step 1

Rewrite the equation as $\frac{\sin (x)}{\sin (x^{2})} = \frac{c}{c^{2}}$ .

$\frac{\sin (x)}{\sin (x^{2})} = \frac{c}{c^{2}}$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Simplify $\frac{\sin (x)}{\sin (x^{2})}$ .

Tap for more steps...

Step 2.1.1

Rewrite $\frac{\sin (x)}{\sin (x^{2})}$ as a product.

$\sin (x) \frac{1}{\sin (x^{2})} = \frac{c}{c^{2}}$

Step 2.1.2

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

$\frac{\sin (x)}{1} \cdot \frac{1}{\sin (x^{2})} = \frac{c}{c^{2}}$

Step 2.1.3

Simplify.

Tap for more steps...

Step 2.1.3.1

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

$\sin (x) \frac{1}{\sin (x^{2})} = \frac{c}{c^{2}}$

Step 2.1.3.2

Convert from $\frac{1}{\sin (x^{2})}$ to $\csc (x^{2})$ .

$\sin (x) \csc (x^{2}) = \frac{c}{c^{2}}$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Cancel the common factor of $c$ and $c^{2}$ .

Tap for more steps...

Step 3.1.1

Raise $c$ to the power of $1$ .

$\sin (x) \csc (x^{2}) = \frac{c^{1}}{c^{2}}$

Step 3.1.2

Factor $c$ out of $c^{1}$ .

$\sin (x) \csc (x^{2}) = \frac{c \cdot 1}{c^{2}}$

Step 3.1.3

Cancel the common factors.

Tap for more steps...

Step 3.1.3.1

Factor $c$ out of $c^{2}$ .

$\sin (x) \csc (x^{2}) = \frac{c \cdot 1}{c \cdot c}$

Step 3.1.3.2

Cancel the common factor.

$\sin (x) \csc (x^{2}) = \frac{c \cdot 1}{c \cdot c}$

Step 3.1.3.3

Rewrite the expression.

$\sin (x) \csc (x^{2}) = \frac{1}{c}$