Question

Write the tangent wave function given the amplitude and period.

a) y = tan(2x)
b) y = tan(x/2)
c) y = tan(0.5x)
d) y = tan(πx)

Answer 1

The tangent wave functions provided are variations of the tan function, each with different periods determined by the coefficient in front of x. The correct option is D.

Step-by-step explanation:

The student has asked to write the tangent wave function given the amplitude and period for several different variations of the tangent function. Response to such a question involves analyzing the influence of different coefficients and constants within the function on its amplitude and period.

• Amplitude refers to the maximum distance from the axis of oscillation in the wave, and in the case of tangent functions, amplitude isn't as clearly defined because the function's range is all real numbers, and it does not have a maximum value.
• The period of a tangent function, on the other hand, is dictated by the coefficient in front of the variable x. The period of a basic tan(x) function is π, but when the function is y = tan(bx), the period becomes π/b.

Based on this understanding:

1. y = tan(2x) would have a period of π/2.
2. y = tan(x/2) would have a period of 2π.
3. y = tan(0.5x) is the same as y = tan(x/2), so its period is also 2π.
4. y = tan(πx) would have a period of 1.