Trigonometry Examples

$\cot (\arcsin (x))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - x^{2}}, x)$ , $(\sqrt{1^{2} - x^{2}}, 0)$ , and the origin. Then $\arcsin (x)$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - x^{2}}, x)$ . Therefore, $\cot (\arcsin (x))$ is $\frac{\sqrt{1 - x^{2}}}{x}$ .

$\frac{\sqrt{1 - x^{2}}}{x}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{\sqrt{1^{2} - x^{2}}}{x}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

$\frac{\sqrt{(1 + x) (1 - x)}}{x}$