# Graphing Trigonometric Functions

```Graphing Trigonometric
Functions
BY MICRO, FOU AND NONG 10A
Find the amplitude and the period
of sine and cosine graph

To find the amplitude and the period, you must need to look at the
equation.
𝑦 = 𝛼 sin 𝑏 𝜃 / 𝑦 = 𝛼 cos 𝑏 𝜃
amplitude

Amplitude =

360°
Period =
𝑏
𝑎
amplitude
Exercise 1

What is the amplitude and the period of 𝑦 = 2 sin 3 (𝜃).
A
Amplitude = 1
Period = 60°
B
Amplitude = 2
Period = 120°
C Amplitude = 3
Period = 180°
D
Amplitude = 4
Period = 240°
Exercise 2

What is the amplitude and the period of 𝑦 = 3 cos 2 (𝜃).
A
Amplitude = 1
Period = 60°
B
Amplitude = 2
Period = 120°
C Amplitude = 3
Period = 180°
D
Amplitude = 4
Period = 240°
How to graph trigonometry
function

In 𝑠𝑖𝑛𝑒, the graph start from 0 while in cos the graph start from the
first letter of the equation.
Example:
𝑦 = 2 sin 3 (𝜃) , the graph will start from the zero because the graph is
sin .
𝑦 = 2 𝑐𝑜𝑠 3 (𝜃) , the graph will start from two because the graph is 𝑐𝑜𝑠 .

To draw a graph, we need to find amplitude and the period.
Example: 𝑦 = 2 sin 3 (𝜃)
Amplitude = 2 , Period = 120°
How to graph trigonometry
function
𝑦 = 2 sin 3 (𝜃)
Amplitude = 2 , Period = 120°
Exercise 3

A
Find the graph of 𝑦 = 3 sin 6 (𝜃)
B
Exercise 4

A
Find the graph of 𝑦 = cos 2(𝜃)
B
Tangent graph

It is in the form of y= tan 𝜃

Has no amplitude

Has the period of 180 °
Find period and asymptote of the
function

To find the period, the method is the same but the only change is
you change 360 ° to 180 °.
𝑦 = 𝑡𝑎𝑛 𝑏 𝜃
180°
 Period =
𝑏
180°
 Asymptote =
2𝑏

The graphing method of tangent is the same as sine and cosine but
instead of amplitude, you need to sketch the asymptote first and
then draw the actual function.
Exercise 5

What is the amplitude and the period of 𝑦 = tan 3 (𝜃).
A
Asymptote = every 30 °
Period = 60°
B
Asymptote = every 60 °
Period = 60°
C Asymptote = every 90 °
Period = 60°
D
Asymptote = every120 °
Period = 60°
Exercise 6

A
Find the graph of 𝑦 = 𝑡𝑎𝑛 (𝜃)
B
Cosecant and secant graph
To draw the cosecant and secant graph, first you need to locate where is the line y = sin x
meet the zero. That will be the asymptote. After you get the asymptote, you just draw the
graph of y = csc x at the highest and lowest point and between the asymptote.
y
y
𝑦 = sec 𝑥
𝑦 = csc 𝑥
4
4
𝑦 = cos 𝑥
x



2
2

3
2
2
5
2
3
x



2
2
3
2
2
5
2
y  sin x
4
4

Tangent graph
Cotangent graph is just a reflection of the tangent graph.
y
y  cot x

vertical asymptotes
3
2
 

2
x  
x0

 3
2
2
x 
x
2
𝑦 = tan 𝑥
x  2
Thank you
```
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