The cosine of an angle is the x-coordinate of the point where its terminal ray intersects the unit circle. So, we can draw a line at x=-1/2 and see where it intersects the unit circle. That will tell us possible values of θ/2.
We find that vertical line intersects the unit circle at points where the rays make an angle of ±120° with the positive x-axis. If you consider only positive angles, these angles are 120° = 2π/3 radians, or 240° = 4π/3 radians. Since these are values of θ/2, the corresponding values of θ are double these values.
a) The cosine values repeat every 2π, so the general form of the smallest angle will be
... θ = 2(2π/3 + 2kπ) = 4π/3 + 4kπ
b) Similarly, the values repeat for the larger angle every 2π, so the general form of that is
... θ = 2(4π/3 + 2kπ) = 8π/3 + 4kπ
c) Using these expressions with k=0, 1, 2, we get
... θ = {4π/3, 8π/3, 16π/3, 20π/3, 28π/3, 32π/3}
Four times the sum of x and two
Answer:
19/50
Step-by-step explanation:
If you put this in decimal form, it's 0.38.
All you have to do is convert the decimal to a reduced fraction, which is 19 over 50 (19/15).
Hope this helps you!
Answer:
2d
——
cd
Step-by-step explanation:
c - d
Simplify —————
cd
1
Simplify —
d
Equation at the end of step 2 :
1 1 (c - d)
(— + —) - ———————
c d cd
Step 3 :
1
Simplify —
c
Equation at the end of step 3 :
1 1 (c - d)
(— + —) - ———————
c d cd