Trigonometry Help: Reference Angles and Quadrants?

Question

I am having a really, really hard time understanding trigonometry, for some reason I am not grasping any of the concepts that are being taught. Unfortunately I have online classes and I don’t have a teacher to try and explain things to me. If you can please help me out on this problem, I would greatly appreciate it. Thank you so much for your help in advance.


Find the reference angles (theta) for the angles given below.
Find the quadrants in which the angles lie.
In addition, show all the steps for deriving the answer.

1. (theta) = 50 degrees
2. (theta) = 120 degrees
3. (theta) = 6 (pi) / 7
4. (theta) = 3.3
5. (theta) = 300 degrees
6. (theta) = - 145 degrees

Answer 1

Best Answer - Chosen by Asker

The reference angle is the positive acute angle that the terminal side makes with the x-axis. The initial side of your angle is assumed to lie on the positive x-axis.
1) 50° (is in Q I, between 0° and 90°) has reference angle of 50°
2) 120° (is in QII, between 90° and 180°)has reference angle of 60°
(I subtracted 120 from 180.)

3) 6π/7 (is in Q II) has a reference angle of π/7
(I subtracted 6π/7 from π. Notice that
8π/7 (a Q III angle) would have the same reference angle.)
4) 3.3 (is presumed to be radian measure, a pure number without units, like #3; is in Q III) has a reference angle of 0.1584073464102067615373566167205.
(I subtracted your angle from π; then took the absolute value of the negative difference. Alternatively, you could just subtract π from your angle. You can round off to whatever accuracy you require.

5) 300° (is a Q IV angle) with a reference angle of 60° I subtracted 300 from 360.
6) -145° (is a Q III angle; the negative means that you rotate clockwise from the positive x-axis, instead of CCW) has a reference angle of 45° (I know that 145° be it positive or negative is 45° from 180°.)

Hope this helps.
- - - - -
In general, positive angles are measured CCW from the positive x-axis. Negative angles are measured CW from the positive x-axis. With a perpendiular to the x-axis you generate 4 quadrants QI is upper-right;
QII is upper left; Qiii is lower left; Qiv is lower right (you count CCW). ±360° is a complete revolution as is ±2π.

Asker's Rating:

Asker's Comment:

Thank you so much for your help, I really appreciate it. I am not that smart in math and I am having a really hard time understanding a lot of what it being taught, so everything that you have provided has helped me greatly. Thank you again!!