In Exercises 35–60, find the reference angle for each angle. 5...

Question

In Exercises 35–60, find the reference angle for each angle. 553°

Accepted Answer

Hello everybody. I hope you are doing. All right. Today, today we're going to look at this question that states calculate the measurement of the reference angle for 541 degrees. The answer choices provided to us are a 89 degrees B one degree C 46 degrees or D 44 degrees. Now, the first thing we have to do is use our angle and put it in standard form. Now we know it's not in standard form because it falls outside of 360 degrees. So for standard form, so for standard form, all we have to do in this case is use 541 degrees, which is the oven was minus 360 degrees and that will be equal to 181 degrees. And now this is in standard form. So in accordance system, this 181 degrees will fall in the exact same spot as degrees. Now, 181 degrees is an angle that falls in quadrants three. Why? Well, because 180 degrees is less than 181 degrees, which is less than 270 degrees. So the cut-off for quadrant three is 180 degrees and 270 degrees. Why? Well, think of 100 and 80 degrees as the right side of the X axis or the left side of the X axis in a coordinate system and take up 270 degrees as the bottom side of the Y axis. So if you look at those two corners, then 181 degrees will fall in that quadrant. Now, for the reference angle, there's different rules for reference angles depending on which part you're located at. So in quadrant three, our rule states that the reference angle is equal to our angle, the angle given minus 180 degrees. Therefore, we have 181 degrees, which is the angle given minus 180 degrees. And this will be equal to one degree and that will be our answer for this question or as choice B. So we see how simple a question like this could get if we just know how to work in standard form and know our rules for reference angles. So I hope that was helpful. And until next time.

In Exercises 35–60, find the reference angle for each angle. 553°

Key Concepts

Reference Angle

Coterminal Angles

Quadrants and Angle Position

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