Precalculus Examples

$\sec (\arcsin (\frac{21}{29}))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - {(\frac{21}{29})}^{2}}, \frac{21}{29})$ , $(\sqrt{1^{2} - {(\frac{21}{29})}^{2}}, 0)$ , and the origin. Then $\arcsin (\frac{21}{29})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - {(\frac{21}{29})}^{2}}, \frac{21}{29})$ . Therefore, $\sec (\arcsin (\frac{21}{29}))$ is $\frac{29}{20}$ .

$\frac{29}{20}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{20}$

Decimal Form:

$1.45$

Mixed Number Form:

$1 \frac{9}{20}$