Station 1: Finding Info from Trig Equations ... 2014/04/08 آ  Station 1: Finding Info from Trig...

download Station 1: Finding Info from Trig Equations ... 2014/04/08 آ  Station 1: Finding Info from Trig Equations

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Transcript of Station 1: Finding Info from Trig Equations ... 2014/04/08 آ  Station 1: Finding Info from Trig...

  • 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. sin 3y 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.!!! ! ! ! ! ! ! ! 2.!!! ! ! ! ! ! ! ! ! ! ! ! 3.!!! ! ! ! ! ! ! ! 4.!!! ! ! ! ! ! ! ! ! ! ! ! 5.! ! ! ! ! ! ! ! 6.!!! ! ! ! ! ! ! !

    ! ! ! !

    2 !2 !

    2 ! !

    4 ! !

  • Stat ion 3: Tr ig Graph Applicat ions

    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

    Station 2: Finding Equations of Trig Graphs

    1) ! = 2 sin 2! 2) ! = − cos !! 3) ! = −3 sin !! 4) ! = cos 2! + 2 5) ! = 0.5 sin !! − 2 6) ! = −3 sin 2! + 1

    Station 3: Trigonometric Function Applications

    1) f x = − cos !!" x + 9 2) a- 0.75

    b- !!! ! = 12

    c- 6 hours (half the period) d- 1.875 feet e- 1.6 hours & 10.4 hours

  • Station 4: Graphing Trig Functions

    1)

    2)

    3)

    4)