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}
The answer is: B
Hope this helped!
We are trying to find miles/hour, which shows that we are going to be dividing the total number of miles by the total number of hours. Thus, in this case, the miles/hour rate will be:
He drove 40 miles in one hour.
Answer: rectangular prism
Step-by-step explanation:
1035.33156649 meters high is the helicopter flying over the building.
Given that, an observer (O) is located 900 feet from a building (B). The observer notices a helicopter (H) flying at a 49° angle of elevation.
We need to find how high is the helicopter flying over the building.
<h3>How to find the height of the building using trigonometry?</h3>
To measure the heights and distances of different objects, we use trigonometric ratios.
Here, use the Tangent rule to calculate the height of the building.
tan(angle) = opposite/adjacent
Now, tan 49°=h/900
⇒h=1035.33156649 meters
Therefore, 1035.33156649 meters high is the helicopter flying over the building.
To learn more about the angle of elevation visit:
brainly.com/question/21137209.
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