GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A technician is monitoring the voltage of a circuit. The voltage, V, in volts, over time, t, in milliseconds, is given by the function V(t) = 5sin(πt/2) + 12. What is the maximum voltage recorded in the circuit?
- A17 volts
- B12 volts
- C5 volts
- D7 volts
Show answer & explanationAnswer & explanation
Correct answer: A. 17 volts
The sine function, sin(x), has a maximum value of 1. To find the maximum voltage, substitute this maximum value into the function: V_max = 5(1) + 12 = 5 + 12 = 17 volts. The 5 is the amplitude, and 12 is the vertical shift (midline).
Why the other options are wrong
- B. This is the vertical shift or the midline of the sine wave, not the maximum.
- C. This is the amplitude of the sine wave, not the maximum voltage.
- D. This would be the minimum voltage if the vertical shift was 12-5=7.
Range of Trigonometric Functions (with Transformations)
The range of a trigonometric function, especially sine or cosine, is affected by its amplitude (vertical stretch) and vertical shift (midline). The basic sine/cosine functions have a range of [-1, 1].
- For y = A sin(Bx + C) + D, A is the amplitude, D is the vertical shift (midline).
- The maximum value is D + |A|.
- The minimum value is D - |A|.
- The range is [D - |A|, D + |A|].
Memory trick: Max is 'Midline + Amplitude', Min is 'Midline - Amplitude'!