Trigonometric Phase Shifts

The video tutorial explains the shifts in trigonometric functions, focusing on phase and vertical shifts. It introduces the six basic trigonometric functions and describes how to shift their graphs horizontally and vertically. The tutorial details the components of a trigonometric function, specifically amplitude, frequency, phase shift, and vertical shift, with a focus on phase and vertical shifts. Examples illustrate how to apply these shifts to sine and cosine functions, demonstrating the effects on their graphs.

Which of the following is NOT a basic trigonometric function?

• Exponential

• Cosine

• Tangent

• Sine

What does the 'A' component represent in the trigonometric function format?

• Phase Shift

• Frequency

• Vertical Shift

• Amplitude

In the function Y = sin(X - π/4), what is the direction of the phase shift?

• Up π/4 units

• Right π/4 units

• Down π/4 units

• Left π/4 units

For the function Y = cos(X + π/2), how should it be rewritten to identify the phase shift?

• Y = cos(X - π/2)

• Y = cos(X - (-π/2))

• Y = cos(X + π/2)

• Y = cos(X + (-π/2))

When b = 1, what does a positive phase shift indicate?

• The function shifts to the right

• The function shifts upwards

• The function shifts to the left

• The function shifts downwards

What happens to the graph of Y = cos(X - 6) in terms of vertical shift?

• Shifts left by 6 units

• Shifts right by 6 units

• Shifts down by 6 units

• Shifts up by 6 units

Which component is used to move the graph of a trigonometric function up and down?

• D

• A

• B

• C