Question

Question #55edb

Answer 1

The angle should measure `143.13^@`, 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 `3/5`, we can plug this number into our calculator to solve for our reference angle in quadrant I.

`sin^(-1)(3/5) = 36.87^@`

Now, here's the rule:

If the angle is in quadrant II;

`"180 degrees - reference angle = answer"`

And as an extra, quadrant III:

`"180 degrees + reference angle = answer"`

Finally, quadrant IV:

`"360 degrees - reference angle = answer"`

So

`"180 degrees - 36.87 degrees = 143.13 degrees"`

Hope this helps!

Best wishes,
A fellow highschool student.