Page 309 – Amplitude, Period and Phase Shift Objective To find the amplitude, period and phase shift for a trigonometric function To write equations of trigonometric functions given the amplitude, period, and phase shift

Glossary Amplitude Period Phase Shift

Amplitude of Sine and Cosine Functions The amplitude of the functions y = A sin  and y = A cos  is the absolute value of A The tangent, cotangent, secant and cosecant functions do not have amplitudes because their values increase and decrease without bound.

State the amplitude of the function y = 3 cos  Graph  y  3 cos  y = cos  on the same set of axes. Compare the graphs. According to the definition of amplitude, A = 3. Make a table of values.  0°45°90°135° 180° 225° 270° 315°360° cosQ cosQ Graph the points and draw a smooth curve.

Period The period of a function is the distance on the x-axis it takes a function to go through one complete cycle. The period of the functions y = sin k  and y = cos k  is: 360° k The period of the function y = tan k  is: 180° k

State the period of the function y = sin 4 . Then graph the function and y = sin  on the same set of axes. By definition, the period of the sin function is 360°/k. Period = 360°/4 = 90° This means the function y = sin 4  goes through one complete cycle in 90°.

Phase Shift Phase shift moves the graph of the function horizontally. The phase shift of the function y = A sin (k  + c) is: - ckck If c > 0 the shift is to the left. If c < 0 the shift is to the right. This applies to all the trigonometric functions.

State the phase shift of the function y = tan (  – 45). Then graph the function and y = tan  on the same axes and compare. The phase shift is – c/k = 45° Since c is less than 0 the shift is to the right.

Assignment Page 315 –# 4 – 11,