Station 1: Finding Info from Trig Equations Find the amplitude, period, midline, and phase shift of each of the following functions. 1. ! = 4 cos ! + 2! + 3.5 2. sin 3 y x π ⎛ ⎞ = − − ⎜ ⎟ ⎝ ⎠ 3. ( ) 45sin y x π = − 4. ! = ! ! cos 2! + ! ! − 1 5. ! = −3 sin 3! − 2 6. ! = cos ! ! ! − !
6
Embed
Station 1: Finding Info from Trig Equations...2014/04/08 · Station 1: Finding Info from Trig Equations Find the amplitude, period, midline, and phase shift of each of the following
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Stat ion 1: F inding Info f rom Tr ig Equations Find the amplitude, period, midline, and phase shift of each of the following
functions.
1. ! = 4 cos ! + 2! + 3.5 2. sin3
y x π⎛ ⎞= − −⎜ ⎟⎝ ⎠
3. ( )45siny x π= − 4. ! = !! cos 2! + !
! − 1
5. ! = −3 sin 3! − 2 6. ! = cos !! ! − !
S tat ion 2: Writ ing Equations of Tr ig Graphs (no phase shif t )
1) Jacob and Emily ride a Ferris wheel at a carnival in Billings, Montana. The wheel has a 16 meter diameter, and turns at three revolutions per minute, with its lowest point one meter above the ground. Assume that Jacob and Emily's height h above the ground is a sinusoidal function of time t, where t=0 represents the lowest point on the wheel and t is measured in seconds. Write a cosine function for the motion of the ferris wheel.
2) The depth of the water on the shore of a beach varies as the tide moves in and out. The equation ! ! = 0.75 cos !
! ! + 1.5 models the depth of the water, !(!), in feet and t as time in hours.
a) What is the amplitude of the equation?
b) What is the period of the equation?
c) In how many hours will the tide be at its lowest?
d) How deep will the water be 2 hours after the high tide?
e) When will the water be 2 feet deep? (Nearest 10th- use calc!)
Stat ion 4: Graphing Tr ig Funct ions Fill out the missing info & graph each function!
KEY Station 1: Finding Info from Equations
1. amp= 4, midline y=3.5, period 2!, phase shift: 2! left 2. amp= 1, midline y=0, period 2!, phase shift: !! right
3. amp= 45, midline y=0, period 2!, phase shift: ! right
4. amp= !! midline y=-1, period !, phase shift: !! left
5. amp= 3, midline y=0, period !!! , phase shift:!! right
6. amp= 1, midline y=0, period !!, phase shift: !! right