Trigonometry:Graphs of Trig Functions

Honors Precalculus

Mr. Velazquez

The Graph of y = sin 𝑥

Range:[−1, 1]

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

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.

Animation

http://gfycat.com/AliveGroundedCottonmouth

Variations of Sine and Cosine

Variations of Sine and Cosine

𝑥

𝑦

𝜋

2𝜋 3𝜋

22𝜋

Graph one period of the

function 𝒚 = 𝟒 𝐬𝐢𝐧 𝟐𝒙 −𝟐𝝅

𝟑

Variations of Sine and Cosine

Variations of Sine and Cosine

𝑥

𝑦

𝜋

2𝜋 3𝜋

22𝜋

Graph one period of the

function 𝒚 =𝟏

𝟐𝐜𝐨𝐬 𝟒𝒙 + 𝝅

Graph of 𝑦 = tan 𝑥

Graph of 𝑦 = tan 𝑥

Variations of 𝑦 = tan 𝑥

Variations of 𝑦 = tan 𝑥

Variations of 𝑦 = tan 𝑥

𝑥

𝑦

𝜋

2𝜋 3𝜋

22𝜋

Graph 𝑦 = − tan 2𝑥

Variations of 𝑦 = tan 𝑥

𝑥

𝑦

𝜋

2𝜋 3𝜋

22𝜋

Graph 𝑦 = tan 𝑥 −𝜋

2

Graph of 𝑦 = cot 𝑥

Variations of 𝑦 = cot 𝑥

Variations of 𝑦 = cot 𝑥

𝑥

𝑦

𝜋

2𝜋 3𝜋

22𝜋

Graph 𝑦 = cot 𝑥 − 𝜋

Variations of 𝑦 = cot 𝑥

𝑥

𝑦

𝜋

2𝜋 3𝜋

22𝜋

Graph 𝑦 = 2cot 𝑥 −𝜋

4

Graph of 𝑦 = csc 𝑥

Graph of 𝑦 = sec 𝑥

Variations of Secant and Cosecant

Variations of Secant and Cosecant

Variations of Secant and Cosecant

𝑥

𝑦

𝜋

2𝜋 3𝜋

22𝜋

Graph 𝑦 = sin 2𝑥and its reciprocal

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