Question

Trig: Finding Reference Angle

http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Coterminal%20Angles%20and%20Reference%20Angles.pdf

Can you help me with #1 and #2

Answer 1

I obviously can see the answers but I do not understand how they are getting the answer.

Answer 2

I was trying to see if I could work backwards.

Answer 3

1) -230 degrees. Falls in second quadrant. -230 = -180 - 50
So angle with x axis is 50 degrees.

Answer 4

Wait but why are you using 180?

Answer 5

We need to find the angle between the line and the nearest x axis (that is with the positive x-axis or the negative x-axis). -230 falls in the second quadrant. So starting from positive x axis, if we go -180 we get to the negative x axis and we need to go 50 more degrees to get to our line. So x2 = 50. The reference angle is always expressed as a positive quantity.

Answer 6

Or if you want to go the positive route then -230 is same as -230 + 360 = +130 degrees. So what will x2 be? 180 - 130 = 50 degrees.

Answer 7

So will the reference angle always deal with 180 degrees?

Answer 8

In the 4th quadrant it will involve 360 degrees. In the second and third quadrant, it will involve 180 degrees.

Answer 9

So in the first it will deal with 90?

Answer 10

Some examples:
Line makes 60 degrees. Quadrant 1. RA = 60 degrees
Line makes 130 degrees. Quadrant 2. RA = 180 - 130 = 50 degrees
Line makes 240 degrees. Quadrant 3. RA = 240 - 180 = 60 degrees
Line makes 320 degrees. Quadrant 4. RA = 360 - 320 = 50 degrees

So in quadrants 1 and 4 we find how much angle it makes with positive x-axis.
In quadrants 2 and 3 we find how much angle it makes with negative x-axis.

Answer 11

360-320 = 40 degrees (in the last example)

Answer 12

So let me try number 6.

Answer 13

640 degrees is in the 4th quadrant.

Answer 14

The angle will never be 90 or greater right?

Answer 15

correct. But first reduce the angle to between 0 and 360 degrees (or 0 and 2pi) by taking out as many multiples of 360 (or multiples of 2pi radians) and then use the above method.

Answer 16

640 - 360 = 280 degrees.

Answer 17

Which is located in the third quadrant

Answer 18

No third stops at 270 degrees.

Answer 19

Oops

Answer 20

So fourth quadrant

Answer 21

360 - 280 = 80 degrees

Answer 22

Yes, whichever quadrant you start with, by taking out as many 360 degrees or adding as many 360 degrees you wind up in the exact same position.

Yes 80 degrees is the reference angle.

Answer 23

Can I try number 4?

Answer 24

go ahead.

Answer 25

I will convert this to degrees first.

Answer 26

Which equals -290

Answer 27

-290 + 360 = 70 degrees

Answer 28

then I will change it back to radians
7pi/18

Answer 29

This is in radians. So 360 will be 2pi. 180 will be pi.
You can do it in radians or degrees. If they give the angle in degrees your final answer should be in degrees. If radians then you should give in radians.

Answer 30

my answer is radians right? 7pi/18

Answer 31

Yes, you got it.

Answer 32

Thank You so much... why can't you be the teacher at my school?

Answer 33

Without changing it to degrees you can do the same problem like this:
-29pi/18. You can add or subtract 2pi radians without affecting the angle as it will end up in the same place. Add 2pi
-29pi/18 + 2pi = (-29pi + 36pi) / 18pi = 7pi/18.

You are welcome.