Trigonometry Examples

$\tan (arcsec (4))$

Step 1

Draw a triangle in the plane with vertices $(1, \sqrt{4^{2} - 1^{2}})$ , $(1, 0)$ , and the origin. Then $arcsec (4)$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, \sqrt{4^{2} - 1^{2}})$ . Therefore, $\tan (arcsec (4))$ is $\sqrt{4^{2} - 1}$ .

$\sqrt{4^{2} - 1}$

Step 2

Raise $4$ to the power of $2$ .

$\sqrt{16 - 1}$

Step 3

Subtract $1$ from $16$ .

$\sqrt{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{15}$

Decimal Form:

$3.87298334 \dots$