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}
X=18 , first you have to rewrite it as fractions then you have to cross multiply the equation , and last divide
Answer:
0.430 (nearest thousandth)
Step-by-step explanation:
Using binomial probability relation :
p = 0.81
n = 4
x = 4
1 - p = 1 - 0.81 = 0.19
Recall ;
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 4) = 4C4 * 0.81^4 * 0.19^(4-4)
P(x = 4) = 1 * 0.43046721 * 1
P(x = 4) = 0.43046721
P(x = 4) = 0.430 (nearest thousandth)