ss_5_6

ss_5_6 - Section 5.6 Sinusoidal Graphs This section...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 5.6 Sinusoidal Graphs This section contains analysis of sine and cosine as periodic functions. Definition. If f ( t )= A sin ωt and g ( t )= A cos ωt , then the number | A | is called the amplitude of f and g , and the number T = 2 π ω , ω> 0, is called the period of f and g . •| A | Amplitude of A sin ωt , A cos ωt T = 2 π ω ( ω> 0) Period of A sin ωt , A cos ωt Note. The above formula for the period can be obtained as follows. The functions f ( t )=sin ωt and g ( t )=cos ωt complete one full cycle when ωt changes from ωt =0to ωt =2 π . This change in ωt occurs when t changes from t =0to t = 2 π ω . Example. Find the amplitude and period of y = - 2sin3 t . Solution. y = - 2sin3 t is of form y = A sin ωt with A = - 2and ω = 3. Hence the amplitude is | A | = 2 and the period is T = 2 π 3 . The graph of this function is shown below. –2 –1 0 1 2 y –3 –2 –1 1 2 3 t y = - 2sin3 t Example. Find the amplitude and period of y =3cos( - 2 t ). Solution. Write y =3cos( - 2 t ) in the form y =3cos(2 t ). (The last step is permissible because the cosine is an even function.) The amplitude is
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

Page1 / 4

ss_5_6 - Section 5.6 Sinusoidal Graphs This section...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online