Translating Trig Graphs - Kuta Software

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©E V2W0K1A2v JKauctxa0 4S8oCfrtwwVaXrWeJ wLHLHCS.8 v kArlGlz PrQizgNhxtXs3 5rGekskeJrNvEeJdd.J D xMSadd7eH kwTiatrh6 vIrnAfqiEnciYtje5 PAtlYgaexbLrwat E2Z.n Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Translating Graphs of Trig Functions
Using degrees, find the amplitude and period of each function. Then graph.
1) y = sin (θ − 135)
2) y = cos (θ − 30)
Date________________ Period____
6
6
5
5
4
4
3
3
2
2
1
1
−1
90° 180° 270° 360° 450° 540°
−1
90° 180° 270° 360° 450° 540°
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
3) y = −2 + tan θ
4) y = 1 + sin θ
6
5
4
3
2
1
6
5
4
3
2
1
−1
60° 120° 180° 240° 300° 360°
−1
90° 180° 270° 360° 450° 540°
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
5) y = 2 + 1 csc (θ − 135)
2
6) y = 2 + 4cos (θ + 90)
6
6
5
4
3
2
1
−1
−2
−3
−4
−5
90° 180° 270° 360° 450° 540°
5
4
3
2
1
−1
−2
−3
−4
−5
−6
90° 180° 270° 360° 450° 540°
−6

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7) y = 1 + cot (2θ − 90)
8) y = 1 + sec
( θ 2 − 135 )
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
60° 120° 180° 240° 300° 360°
6
5
4
3
2
1
−1
−2
−3
−4
−5
180° 360° 540° 720° 900° 1080°
−6
Using radians, find the amplitude and period of each function. Then graph.
9) y = 1 2 sin ( 3θ + π 4 ) + 1
10) y = 3sec
( θ 2 − 5π 6 ) − 2
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
π
2
π
3π
2
2π
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
π 2π 3π 4π 5π 6π
11) y = 4cos
( 2θ − 5π 6 ) − 2
12) y = 1 2 tan ( 2θ − 5π 3 ) + 1
6
5
4
3
2
1
6
5
4
3
2
1
−1
−2
π
2
π
3π
2
2π
−1
−2
π
2
π
3π
2
2π
−3
−3
−4
−4
−5
−5
−6
−6

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©3 c2j0K1D2q UKgudtCaz cSvoUfGtJwcarrMeE LL1LXCW.Z q eAulAlk irVihgShwtesS rrge4sjeYr avqeJdl.L Z hMcapdZez RwNiOtKhO KIGnzf5iYneihtieU qAalAgieUbVr5aB 22t.R Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Translating Graphs of Trig Functions
Using degrees, find the amplitude and period of each function. Then graph.
1) y = sin (θ − 135)
2) y = cos (θ − 30)
Date________________ Period____
6
Amplitude: 1
Period: 360°
6
Amplitude: 1
Period: 360°
5
5
4
4
3
3
2
2
1
1
−1
90° 180° 270° 360° 450° 540°
−1
90° 180° 270° 360° 450° 540°
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
3) y = −2 + tan θ
4) y = 1 + sin θ
6
Amplitude: None
Period: 180°
6
Amplitude: 1
Period: 360°
5
5
4
4
3
3
2
2
1
1
−1
60° 120° 180° 240° 300° 360°
−1
90° 180° 270° 360° 450° 540°
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
5) y = 2 + 1 csc (θ − 135)
2
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
90° 180° 270° 360° 450° 540°
Amplitude: None
Period: 360°
6) y = 2 + 4cos (θ + 90)
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
90° 180° 270° 360° 450° 540°
Amplitude: 4
Period: 360°

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©U F2x01102G QKAupt3af jSLoFfDtRwIavr3ew rL0L8C4.D c nAGlJlV ar7iIgLh9t0sA Xr3evsYePrevqeWdF.e I XMdaYd5e6 MwyiPtuhM fIwnWf5ipn6intEe9 aAwlHgceJbPrCaH a2S.0 Worksheet by Kuta Software LLC
7) y = 1 + cot (2θ − 90)
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
60° 120° 180° 240° 300° 360°
Amplitude: None
Period: 90°
8) y = 1 + sec
( θ 2 − 135 )
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
180° 360° 540° 720° 900° 1080°
Using radians, find the amplitude and period of each function. Then graph.
Amplitude: None
Period: 720°
9) y = 1 2 sin ( 3θ + π 4 ) + 1
10) y = 3sec
( θ 2 − 5π 6 ) − 2
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
π
2
π
3π
2
2π
Amplitude: 1 2
Period: 2π 3
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
π 2π 3π 4π 5π 6π
Amplitude: None
Period: 4π
11) y = 4cos
( 2θ − 5π 6 ) − 2
12) y = 1 2 tan ( 2θ − 5π 3 ) + 1
6
5
Amplitude: 4
Period: π
6
5
Amplitude: None
Period: π 2
4
4
3
3
2
2
1
1
−1
−2
π
2
π
3π
2
2π
−1
−2
π
2
π
3π
2
2π
−3
−3
−4
−4
−5
−5
−6
−6
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