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

5.5

Question

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

5.5

Accepted Answer

Hello everybody at Howard and I today today, we're going to look at this question that states calculate the measurement of the reference angle for 6.7 and express the answer in four significant figures where the answer choices are a 0. B 12.98 C 3.558 N D 9.842. Now, the first thing I want to do here is look at my, the angle that they gave me. So they gave me 6.7 and there is no degrees. So that means that we're going to be working with radiant. Now, 6.7 is greater than two pie and two pie is the same thing as saying 360 degrees. So two pie is as if you went around the entire an entire plot. So we have to get this into its standard form. So if we're working with radiant and they give us an angle that is greater than two pi we have to get it into its standard form. And you do that by getting the angle in this case 6.7 and subtracting two pi from it. So we have 6.7 minus two pi and that will come out to be around 0.4168. And so on. Now, we want to convert this to the degrees to see exactly where or what quadrant we are in. Now to convert to degrees, you get the radiance or I'll write a general formula first. So converting to degrees will be radiance multiplied by open parentheses, 180 degrees divided by pi and closed parentheses. So this will be equal to 0.4168, multiplied by 180 divided by pi. And once we do that multiplication, this will come out to be around 23. degrees. So that is the degree version of the angle that we are working with in its standard form. Now we know that zero degrees is less than 23. So in, in trying to see where what quadrant we're in, we use the angle that we have. So 23.88 and 23.88 is greater than zero degrees, but less than 90 degrees. And I use these two values because zero degrees represents the right side of the X axis. So to the right of the y axis and 90 degrees represents the upper side of the Y axis. So above the X axis, and if we're working between those two sides, so the upper side of the Y axis and the right side of the x axis. We will therefore, this will mean that therefore 23.88 degrees falls in quadrants one. And now we can look at actually calculating the reference angle. So each quadrant will have its own rules on how to calculate the reference angle. We are working with quadrant one. So we will focus on the rule for a quadrant one. Now the rule for quarter one says that the reference angle is equal to the angle itself. So we don't have to do any more calculations. We have the value of the angle which is 23.88. However, we are working on radiance so we'll leave it as radiance, which we said was 0.4168. And that will be the answer for the reference angle or answer choice. A so all we had to do was transform our angle to its standard form, then convert it to degrees to see what quadrant we are working with and then use the reference angle formula for that specific quadrant. So I hope that was helpful. And until next time.

In Exercises 35–60, find the reference angle for each angle. 5.5

Key Concepts

Reference Angle

Quadrants of the Coordinate Plane

Trigonometric Functions

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