Trig Graphs & Transformations

Front

What is the general form of a sine function?

Back

The general form of a sine function is y = a * sin(bx - c) + d, where: - a = amplitude - b = frequency - c = phase shift - d = vertical shift.

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak (or trough). It is represented by the absolute value of 'a' in the function y = a * sin(bx - c) + d.

Front

How do you determine the period of a sine or cosine function?

Back

Front

What effect does changing the value of 'a' have on the graph of a sine function?

Back

Changing the value of 'a' affects the amplitude of the graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, the graph opens downwards.

Front

What is the vertical shift in the function y = a * sin(bx - c) + d?

Back

The vertical shift is represented by 'd'. It moves the graph up or down on the y-axis.

Front

What is the phase shift in the function y = a * sin(bx - c) + d?

Back

Front

What is the amplitude of the function y = 3 * cos(2x)?

Back

The amplitude is 3, which is the absolute value of the coefficient of the cosine function.

Front

What is the period of the function y = 4 * sin(5x)?

Back

Front

How does a negative sign in front of a sine function affect its graph?

Back

A negative sign reflects the graph across the x-axis.

Front

What is the amplitude and period of the function y = 2 * cos(3x)?

Back