Trigonometry Examples

$arccot (x) = \arctan (\frac{4}{3})$

Step 1

Take the inverse arccotangent of both sides of the equation to extract $x$ from inside the arccotangent.

$x = \cot (\arctan (\frac{4}{3}))$

Step 2

Simplify the right side.

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Step 2.1

Draw a triangle in the plane with vertices $(1, \frac{4}{3})$ , $(1, 0)$ , and the origin. Then $\arctan (\frac{4}{3})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, \frac{4}{3})$ . Therefore, $\cot (\arctan (\frac{4}{3}))$ is $\frac{3}{4}$ .

$x = \frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$