Precalculus Examples

$\csc (\arccos (3))$

Step 1

The equation for cosine is $\cos (A) = \frac{Adjacent}{Hypotenuse}$ . The inside trig function is $\arccos (3)$ , which means $\cos (A) = 3$ . Comparing $\cos (A) = \frac{Adjacent}{Hypotenuse}$ with $\cos (A) = 3$ , find $Adjacent = 3$ and $Hypotenuse = 1$ . Then, using the pythagorean theorem, find $Opposite = 2 i \sqrt{2}$ .

$Adjacent = 3$

$Opposite = 2 i \sqrt{2}$

$Hypotenuse = 1$

Step 2

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

$\csc (A) = \frac{1}{2 i \sqrt{2}}$

Step 3

Simplify.

$- 0.35355339 i$