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:
C. 20480
Step-by-step explanation:
so the equation is (60x3) divided by 15 because there are 3 minutes and 60 seconds in each minute and the bacteria doubles every 15 seconds so when you get your answer (12) that is how many times you will double 5.
A multiple of 4 is a 12/50 chance and a multiple of 5 is a 10/50 chance or simplified 1/5 chance
Answer:
7 hours
Step-by-step explanation:
120 x 7 = 840
Find ever origin and then multiplying by the <span>scale factor of 2 and i promise you will get your answer</span>