What is the period of the trigonometric function: f(x) = 4 sin(3x - pi/2) + 7?
Answer and explanation
Correct answer: D. 2pi / 3
- Step 1: The standard form of a sinusoidal function is y = A sin(Bx - C) + D.
- Step 2: The period T of a sine function depends solely on the frequency coefficient B: T = 2pi / |B|.
- Step 3: Here, B = 3.
- Step 4: Therefore, Period T = 2pi / 3.
Answer
2pi / 3.
Why not the others: '2pi' is the period of the parent function sin(x); '3pi / 2' inverts the coefficient; 'pi / 3' divides pi by 3 (which would be the period of tangent).
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