At how many points is sinθ = 1/2 on the interval [-3π, 3π]?
At how many points is sinθ = 1/2 on the interval [-3π, 3π]?
A. 6 points
B. 3 points
C. 12 points
D. 1 point
That's not even an answer choice
The points where sinθ = 1/2 on the interval [-3π, 3π] are θ = π/6, 5π/6, 7π/6, and 11π/6. These points correspond to the angles in the unit circle where the sine function takes on the value of 1/2.
At how many points is sinθ = 1/2 on the interval [-3π, 3π]?
The sine function has a period of 2π and repeats every 2π. The values of sinθ = 1/2 occur at θ = π/6 and θ = 5π/6 in the interval [-3π, 3π]. Since these values repeat every 2π, there are only 2 distinct points where sinθ = 1/2 in the interval [-3π, 3π].
Therefore, the correct answer is:
B. 2 points
I apologize for the oversight. Let's reconsider the question:
At how many points is sinθ = 1/2 on the interval [-3π, 3π]?
The solutions to the equation sinθ = 1/2 on the interval [-3π, 3π] are θ = π/6 and θ = 5π/6, as these are the angles where sine is equal to 1/2 within the given interval.
Thus, there are 2 points on the interval [-3π, 3π] where sinθ = 1/2.
Therefore, the correct answer is:
B. 2 points