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Trigonometry:Graphs of Trig Functions
Honors Precalculus
Mr. Velazquez
The Graph of y = sin 𝑥
The Graph of y = cos 𝑥
The Graphs of Sine and Cosine
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
Variations of Sine and Cosine
Variations of Sine and Cosine
Variations of Sine and Cosine
Variations of Sine and Cosine
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
1
−1
For the next examples, we will be making use of the coordinate system to the right (note the labels on the axes). Copy this graph and follow along with me.
Variations of Sine and Cosine
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
1
−1
Graph:
𝑦 =1
2sin 𝑥
Variations of Sine and Cosine
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph:
𝑦 = cos 𝑥 −𝜋
2
Variations of Sine and Cosine
𝑥
𝑦
𝜋
2𝜋 3𝜋
22𝜋
Graph: 𝑦 = 3 cos 2𝑥
The Graph of 𝑦 = tan 𝑥
The Graph of 𝑦 = tan 𝑥
Variations of Tangent
Variations of Tangent
Variations of Tangent
Variations of Tangent
The Graph of 𝑦 = cot 𝑥
Variations of Cotangent
Variations of Cotangent
The Graph of 𝑦 = csc 𝑥
The Graph of 𝑦 = sec 𝑥
Variations of Secant and Cosecant
Variations of Secant and Cosecant
The Graphs of the Trig Functions
The Graphs of the Trig Functions
Classwork & Homework
Classwork: Graphs of Sine and Cosine: On a separate sheet of paper, graph the following trig functions on the
same set of axes:
(1) 𝑓(𝑥) = 2 sin 𝑥 − 𝜋 (2) 𝑔 𝑥 = −cos 2𝑥 (3) ℎ 𝑥 =1
2tan 𝑥 +
𝜋
2
Homework:Trigonometry HW 2
(MathXL)
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