Trigonometry Examples

$y = \tan (arcsec (2))$

Step 1

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

$y = \sqrt{2^{2} - 1}$

Step 2

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

$y = \sqrt{4 - 1}$

Step 3

Subtract $1$ from $4$ .

$y = \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \sqrt{3}$

Decimal Form:

$y = 1.73205080 \dots$