Finding Coterminal Angles...3

Section 4.1

 

29a
120° = 2/3 π ≈ 0.667 π
Positive coterminal angles: 480°, 840°, 1200°, 1560°... (so, it's not 240 °)
Negative coterminal angles: -240°, -600°, -960°, -1320°...

29b correct

here are some notes for you:

How to find a coterminal angle between 0 and 360° (or 0 and 2π)?

the coterminal angles formula, β = α ± 360 * k

To determine the coterminal angle between 0 and 360°, all you need to do is to use a modulo operation - in other words, divide your given angle by the 360° and check what the remainder is.

We'll show you how it works with two examples - covering both positive and negative angles. We want to find a coterminal angle with a measure of θ such that 0° ≤ θ < 360°, for a given angle equal to:
420°

420 mod 360 = 60°
How to do it manually?

First, divide one number by the other, rounding down (towards the floor): 420/360 = 1
Then, multiply the divisor by the obtained number (called the quotient): 360 * 1 = 360
Subtract this number from your initial number: 420 - 360 = 60
Substituting these angles into the coterminal angles formula gives 420° = 60° + 360° * 1

If you want to find a few positive and negative coterminal angles, you need to subtract or add a number of complete circles. But how many?

One method is to find the coterminal angle in the [0,360°) range (or [0,2π) range), as we did in the previous paragraph (if your angle is already in that range, you don't need to do this step). Then just add or subtract 360°, 720°, 1080°... (2π,4π,6π...), to obtain positive or negative coterminal angles to your given angle. For example, if α = 1400°, then the coterminal angle in the [0,360°) range is 320° - which is already one example of a positive coterminal angle.

-other positive coterminal angles are 680°, 1040°...
-other negative coterminal angles are -40°, -400°, -760°

 

Thank you. I will practice a few more questions.