Trigonometry Examples

$\frac{\sin (\frac{π}{2} + x)}{\sin (π - x)} = \cot (x)$

Step 1

Simplify $\frac{\sin (\frac{π}{2} + x)}{\sin (π - x)}$ .

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Step 1.1

Rewrite $\frac{\sin (\frac{π}{2} + x)}{\sin (π - x)}$ as a product.

$\sin (\frac{π}{2} + x) \frac{1}{\sin (π - x)} = \cot (x)$

Step 1.2

Write $\sin (\frac{π}{2} + x)$ as a fraction with denominator $1$ .

$\frac{\sin (\frac{π}{2} + x)}{1} \cdot \frac{1}{\sin (π - x)} = \cot (x)$

Step 1.3

Simplify.

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Step 1.3.1

Divide $\sin (\frac{π}{2} + x)$ by $1$ .

$\sin (\frac{π}{2} + x) \frac{1}{\sin (π - x)} = \cot (x)$

Step 1.3.2

Convert from $\frac{1}{\sin (π - x)}$ to $\csc (π - x)$ .

$\sin (\frac{π}{2} + x) \csc (π - x) = \cot (x)$

Step 2

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

$x \approx - 0.1, 0.1, - \frac{1}{5}, \frac{1}{5}, - 0.3, 0.3, \frac{2}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x \approx - 0.1, 0.1, - \frac{1}{5}, \frac{1}{5}, - 0.3, 0.3, \frac{2}{5}$

Decimal Form:

$x \approx - 0.1, 0.1, - 0.2, 0.2, - 0.3, 0.3, 0.4$

Step 4