In Exercises 35–60, find the reference angle for each angle.7𝜋4

Question

Accepted Answer

Hello everybody. I hope you're doing tonight today. Today, we're going to look at this question that states calculate the measurement of the reference angle for 11 pi divided by six, where the answer choices provided are a two pi divided by three B five pi divided by four C pi divided by six and D three pi divided by eight. Now, the first thing I want to do here is see where our current angle 11 pi divided by six lies. So in which specific quadrants of a plot, will this angle be? Now? 11 pie divided by six is less than 12 pie divided by six. And I use 12 pi divided by six because T 12 pi is the same as saying two pi which is the right side of the X axis and 11 pi or divided by six is greater than nine pie divided by six. And I use nine pi divided by six because that is the bottom half of the Y axis. So if we're between the bottom half of the Y axis and the right side of the X axis, we know that 11 pi divided by six balls in quadrants four So now that I have that noted, I can go ahead and actually start calculating the reference angle. Now, different quadrants have their own rules for how to calculate the reference angle. So for this case, we're only gonna talk about the rule for quadrant four. So quadrant four states that the reference angle is equal to 180 degrees or actually because we're in quadrant four and because we are dealing with radiance, so we're not dealing with degrees. The reference angle for quadrant four will be two pi minus the angle that we currently have. So this will be equal to two pi minus 11 pi divided by six. I remember two pi is the right side of the X axis. So it's the same thing as if you said 360 degrees, you went all around each quadrant and now you reach the X axis once again. Now this will be equal to two pi is the same thing as saying, 12 pi divided by six minus 11 pi divided by six, which means that we will leave, we'll find finally have an answer that's pi divided by six. So our reference angle here will be pi divided by six or as a choice C. So by just figuring out where our angle or what quadrant or angle falls in and using the specific rule for the reference angle in that quadrant, we were able to figure out the value of our reference angle So, I hope that was helpful and until next time.

In Exercises 35–60, find the reference angle for each angle.7𝜋4

Key Concepts

Reference Angle

Angle Measurement in Radians

Quadrants of the Coordinate Plane

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