Trigonometry Examples

$\tan (arcsec (9))$

Step 1

Draw a triangle in the plane with vertices $(1, \sqrt{9^{2} - 1^{2}})$ , $(1, 0)$ , and the origin. Then $arcsec (9)$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, \sqrt{9^{2} - 1^{2}})$ . Therefore, $\tan (arcsec (9))$ is $\sqrt{9^{2} - 1}$ .

$\sqrt{9^{2} - 1}$

Step 2

Raise $9$ to the power of $2$ .

$\sqrt{81 - 1}$

Step 3

Subtract $1$ from $81$ .

$\sqrt{80}$

Step 4

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 4.1

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

Step 4.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$4 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$