Trigonometry Examples

$\arccos (x) = \arctan (\frac{9}{40})$

Step 1

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

$x = \cos (\arctan (\frac{9}{40}))$

Step 2

Simplify the right side.

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Step 2.1

Draw a triangle in the plane with vertices $(1, \frac{9}{40})$ , $(1, 0)$ , and the origin. Then $\arctan (\frac{9}{40})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, \frac{9}{40})$ . Therefore, $\cos (\arctan (\frac{9}{40}))$ is $\frac{40}{41}$ .

$x = \frac{40}{41}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{40}{41}$

Decimal Form:

$x = 0.\overline{97560}$