trigonometry: graphs of trig functions · classwork: graphs of trig functions homework: pg. 546-547...
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Trigonometry:Graphs of Trig Functions
Honors Precalculus
Mr. Velazquez
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The Graph of y = sin 𝑥
Range:[−1, 1]
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The Graph of y = cos 𝑥
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The Graphs of Sine and Cosine
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Variations of Sine and Cosine
𝑦 = 𝐴 sin𝐵𝑥 𝑦 = 𝐴 cos𝐵𝑥
The graph of 𝑦 has an amplitude of |𝑨| and a period of 𝟐𝝅
𝒃.
𝑦 = 2 sin 𝑥
𝑦 = sin 𝑥
𝑦 = ൗ1 2 sin 𝑥
𝑦 = sin 𝑥𝑦 = sin 𝑥
𝑦 = −2sin 𝑥
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Variations of Sine and Cosine
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
For the next examples, we will be making use of the coordinate system to the right. Copy this graph and follow along with me.
![Page 8: Trigonometry: Graphs of Trig Functions · Classwork: Graphs of Trig Functions Homework: Pg. 546-547 #2-40 (mult. of 2) Graph one period for the following trig functions, along with](https://reader036.vdocuments.site/reader036/viewer/2022063003/5f6097fa65498d31473ec34a/html5/thumbnails/8.jpg)
Variations of Sine and Cosine
![Page 9: Trigonometry: Graphs of Trig Functions · Classwork: Graphs of Trig Functions Homework: Pg. 546-547 #2-40 (mult. of 2) Graph one period for the following trig functions, along with](https://reader036.vdocuments.site/reader036/viewer/2022063003/5f6097fa65498d31473ec34a/html5/thumbnails/9.jpg)
Variations of Sine and Cosine
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph one period of the
function 𝒚 = 𝟒 𝐬𝐢𝐧 𝟐𝒙 −𝟐𝝅
𝟑
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Variations of Sine and Cosine
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Variations of Sine and Cosine
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph one period of the
function 𝒚 =𝟏
𝟐𝐜𝐨𝐬 𝟒𝒙 + 𝝅
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Graph of 𝑦 = tan 𝑥
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Graph of 𝑦 = tan 𝑥
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Variations of 𝑦 = tan 𝑥
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Variations of 𝑦 = tan 𝑥
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Variations of 𝑦 = tan 𝑥
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph 𝑦 = − tan 2𝑥
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Variations of 𝑦 = tan 𝑥
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph 𝑦 = tan 𝑥 −𝜋
2
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Graph of 𝑦 = cot 𝑥
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Variations of 𝑦 = cot 𝑥
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Variations of 𝑦 = cot 𝑥
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph 𝑦 = cot 𝑥 − 𝜋
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Variations of 𝑦 = cot 𝑥
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph 𝑦 = 2cot 𝑥 −𝜋
4
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Graph of 𝑦 = csc 𝑥
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Graph of 𝑦 = sec 𝑥
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Variations of Secant and Cosecant
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Variations of Secant and Cosecant
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Variations of Secant and Cosecant
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph 𝑦 = sin 2𝑥and its reciprocal
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Classwork: Graphs of Trig Functions
Homework:
Pg. 546-547
#2-40 (mult. of 2)
Graph one period for the following trig functions, along with their reciprocals:
1. 𝑦 = 3 sin 2𝑥 −𝜋
3
2. 𝑦 =3
2cos 2𝑥 + 𝜋