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}
Answer:
6u^3
Step-by-step explanation:
If Yoshi saves $5 dollars each week for 23 weeks he will have $115
Answer:
$4851
Step-by-step explanation:
rectangular prism volume = length x width x height
1 litre = 1000 cm³
cost = $per litre x litres
v = l x w x h
30cm x 25cm x 42cm = 31500cm³
litres = cm³ / 1000
31500cm³ / 1000 = 31.5 litres
31.5 x $154 = $4851