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:
754
Step-by-step explanation:
If the number in the one's place is 5 or greater, the number is rounded up to the next ten. If the number is less than 5, the number gets rounded down.
754 is the answer because it rounds down to 750 as it is, but if 1 was added to it, it'd be 755 which would round up to 760.
A conditional statement is always true backwards and forwards
Answer:
Two expressions equivalent to 48j + 36.
Use distributive property of multiplication.
<u>Since 6 is the factor, divide each term by 6 to get the other factor;</u>
- 48j + 36 =
- 6*8j + 6*6 =
- 6*(8j + 6) =
- 6*2(4j + 3)
Answer:imma take an educated guess 16.4%