Calculus Examples

$\tan (arcsec (8))$

Step 1

Draw a triangle in the plane with vertices $(1, \sqrt{8^{2} - 1^{2}})$ , $(1, 0)$ , and the origin. Then $arcsec (8)$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, \sqrt{8^{2} - 1^{2}})$ . Therefore, $\tan (arcsec (8))$ is $\sqrt{8^{2} - 1}$ .

$\sqrt{8^{2} - 1}$

Step 2

Raise $8$ to the power of $2$ .

$\sqrt{64 - 1}$

Step 3

Subtract $1$ from $64$ .

$\sqrt{63}$

Step 4

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 4.1

Factor $9$ out of $63$ .

$\sqrt{9 (7)}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 7}$

Step 5

Pull terms out from under the radical.

$3 \sqrt{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{7}$

Decimal Form:

$7.93725393 \dots$