Question #55edb

1 Answer

Answer:

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.

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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.