# Question #55edb

Nov 6, 2017

The angle should measure ${143.13}^{\circ}$, rounded to the nearest hundredth.

#### Explanation:

I keep the CAST abbreviation rule in mind when doing these types of questions. Starting from quadrant IV and going counter-clockwise, the letters determine which trigonometric function will turn out positive in each quadrant.

C osine, A ll, S ine, T angent.

So for background information, it makes sense that sin would be positive in the second quadrant.

If $\theta$ is $\frac{3}{5}$, we can plug this number into our calculator to solve for our reference angle in quadrant I.

${\sin}^{- 1} \left(\frac{3}{5}\right) = {36.87}^{\circ}$

Now, here's the rule:

If the angle is in quadrant II;

$\text{180 degrees - reference angle = answer}$

And as an extra, quadrant III:

$\text{180 degrees + reference angle = answer}$

$\text{360 degrees - reference angle = answer}$
$\text{180 degrees - 36.87 degrees = 143.13 degrees}$