Precalculus Examples

$\sec (\arcsin (\frac{3}{2}))$

Step 1

The equation for sine is $\sin (A) = \frac{Opposite}{Hypotenuse}$ . The inside trig function is $\arcsin (\frac{3}{2})$ , which means $\sin (A) = \frac{3}{2}$ . Comparing $\sin (A) = \frac{Opposite}{Hypotenuse}$ with $\sin (A) = \frac{3}{2}$ , find $Opposite = 3$ and $Hypotenuse = 2$ . Then, using the pythagorean theorem, find $Adjacent = i \sqrt{5}$ .

$Opposite = 3$

$Adjacent = i \sqrt{5}$

$Hypotenuse = 2$

Step 2

Substitute in the known variables for the equation $\sec (A) = \frac{Hypotenuse}{Adjacent}$ .

$\sec (A) = \frac{2}{i \sqrt{5}}$

Step 3

Simplify.

$- 0.89442719 i$