In Exercises 35–60, find the reference angle for each angle.-150°

Question

Accepted Answer

Hello everybody. I hope you're doing tonight today. Today, we're going to be looking at this question that states calculate the measurement of the reference angle for a negative 128 degrees where the answer choices are a 232 degrees. B negative 232 degrees C negative 52 degrees and D 52 degrees. Now, the first thing I want to do here is move our angle and change it to standard form. Now, I know it's not in standard form because it's a negative angle. So to have it in standard form, we add 360 degrees. So we'll have negative 128 degrees plus degrees and that'll be equal to 232 degrees. Now, we look at where 232 degrees falls and we know that 232 degrees falls in quadrant. Now, let's think this through 232 degrees is greater than 180 degrees, but less than 270 degrees. So 232 degrees falls in quadrants three. Now that we know what quadrant, we're working out of, let's talk about a reference angle rule or the specific quadrants. So we have that for quadrant three, the reference angle equals our angle minus 180. Or if we weren't using degrees, it would be the angle minus pi now beca because we are using degrees, we can just go right ahead and plug in our values. So we'll plug in our current angle of 232 degrees minus 180 degrees, which will be equal to 52 degrees, which means that our reference angle for this question is 52 degrees or choice D So by simply putting our angle in its standard form, and then using a reference angle rule that we have for quadrant three, we were able to get the reference angle for this question. So I hope that was helpful. And until next time.

In Exercises 35–60, find the reference angle for each angle.-150°

Key Concepts

Reference Angle

Standard Position of an Angle

Quadrants of the Coordinate Plane

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