3/29/19 10.2N – Graphing Sine and Cosine · PDF file 2019-03-29 · Parent...

Click here to load reader

  • date post

    13-Aug-2020
  • Category

    Documents

  • view

    2
  • download

    0

Embed Size (px)

Transcript of 3/29/19 10.2N – Graphing Sine and Cosine · PDF file 2019-03-29 · Parent...

  • 10.2N – Graphing Sine and Cosine A. Graph Sine and Cosine

    Parent sine graph 𝑓(𝜃) = sin𝜃 Parent cosine graph 𝑓(𝜃) = cos𝜃 Draw the graph and make a table. Draw the graph and make a table.

    θ siny θ=

    B. Transformations 1. From the 4 transformations in 9.1, today we are discussing _____________ and _______________.

    2. What is the general equation for a trigonometric function? __________________________________

    Phase shift and Period:

    Phase Shift = Period=

    3. Which variable in the equation is related to a horizontal shift? ________ • In the parent graph this is: ______

    4. Which variable in the equation is related to a horizontal stretch? ________

    • In the parent graph this is: ______ • This is used to find the period. The formula for period is: ____________ • The period in the parent graph is ______________

    5. Frequency is defined as the number of oscillations or rotations per unit of time.

    • Frequency is the reciprocal of the period. The formula for frequency is __________ • The frequency in the parent graph is _________

    θ cosy θ=

    3/29/19

    ⑧ @ g

    I V • d

    .

    How long is one cycle ? Lit O The IT 31%Zit O The II 3%25 O I O - I 0 I O - I 0 I

    b 9

    horizontal horizontal shift -

    - Cdilation,→= acoscblx - G) td do Opp of b

    t C

    horizontal translation = c horizontal dilation = b

    moves pts right d left - how long it takes to complete ore

    cycleIn table do opp of Cto X - formula to find period =

    . C

    b I IT

    b 21T

    the21T + 21T

    .

  • D. Making the Graph. (Phase Shift and Period) EX. 1) 𝑓(𝜃) = sin(𝜃 + 𝜋)

    Phase Shift_____ b____ Period_____ Freq._____

    θ

    siny θ=

    EX. 2) 𝑓(𝜃) = cos�𝜃 − 𝜋 4 �

    Phase Shift_____ b____ Period_____ Freq._____

    θ

    cosy θ=

    EX. 3) 𝑓(𝜃) = cos 2𝜃

    Phase Shift_____ b____ Period_____ Freq._____

    θ

    cosy θ=

    EX. 4) 𝑓(𝜃) = sin 𝜃 4

    Phase Shift_____ b____ Period_____ Freq._____

    θ

    siny θ=

    - it I FELT It IT I FELT It

    O The it 34722in O Iz IT ZI 21T - IT - it

    - The O 'The it t # I IF IT 7TH 9¥ O I O - I O I O - I 0 I

    -

    • • no

    •Mr I @

    O 2 IF O ¥ 2=QT ¥ O Iz IT 3¥ 21T O Iz IT ZI 21T

    = O IF If IF IT 4 O 21T 41T bit 8T I O - I O I U I O - I 0

    - .

    * .•.µ

    •*#• .

  • EX. 5) 𝑓(𝜃) = −sin 2(𝜃 − 𝜋)

    Phase Shift_____ b____ Period_____ Freq._____

    θ

    siny θ=

    EX. 6) 𝑓(𝜃) = cos 3 �𝜃 + 𝜋 3 �

    Phase Shift_____ b____ Period_____ Freq._____

    θ

    cosy θ=

    - reflect over x-axis

    go down ISI

    it 2 ZEIT it - I 3 It

    Itt IF EL It 21T g- Is

    - II -

    E 0 It¥3 y

    O - I O+1 O I O - I 0 .

    Y•••✓ an a• go .