Calculus Examples

$\sec (\arcsin (\frac{4}{5}))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - {(\frac{4}{5})}^{2}}, \frac{4}{5})$ , $(\sqrt{1^{2} - {(\frac{4}{5})}^{2}}, 0)$ , and the origin. Then $\arcsin (\frac{4}{5})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - {(\frac{4}{5})}^{2}}, \frac{4}{5})$ . Therefore, $\sec (\arcsin (\frac{4}{5}))$ is $\frac{5}{3}$ .

$\frac{5}{3}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$