Q: ❄️Pre-Calculus Unit 7 Graphing Test

Front

What is the period of the function y = sin(kx)?

Back

The period is given by the formula: Period = 2π/k. For example, if k = 2, the period is 2π/2 = π.

Front

Define amplitude in the context of trigonometric functions.

Back

Amplitude is the maximum distance from the midline of the graph to the peak (or trough). It represents the height of the wave.

Front

What is the midline of a trigonometric function?

Back

The midline is a horizontal line that represents the average value of the function. It is the line y = k in the function y = a sin(bx) + k.

Front

How do you determine the amplitude of the function y = a sin(bx)?

Back

The amplitude is the absolute value of 'a'. For example, in y = 3 sin(x), the amplitude is 3.

Front

What is the effect of changing the value of 'b' in the function y = sin(bx)?

Back

Changing 'b' affects the period of the function. The new period is calculated as 2π/b.

Front

What is the equation of a cosine function with an amplitude of 4 and a midline at y = 2?

Back

The equation is y = 4 cos(x) + 2.

Front

If the period of a sine function is 6π, what is the value of 'b' in y = sin(bx)?

Back

The value of 'b' can be found using the formula: Period = 2π/b. Thus, b = 2π/6π = 1/3.

Front

What does it mean for a trigonometric function to be inverted?

Back

An inverted function has a negative amplitude. For example, y = -3 sin(x) is an inverted sine function.

Front

How do you graph the function y = 2 sin(2x)?

Back

To graph y = 2 sin(2x), identify the amplitude (2), period (π), and midline (y = 0). Plot key points based on these values.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are phase-shifted versions of each other. Specifically, sin(x) = cos(x - π/2).