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)