SM015 - 5.5 (Notes Solutions)

5.5 Trigonometric Functions

Friday, July 10, 2020 3:14 PM

Learning Outcomes:
At the end of the lesson, students should be able to
(a) Find domain and range of trigonometric functions
(b) Sketch the basic graph of trigonometric functions such as

, and .
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5.5 Trigonometric Functions Page 1

Sine Function,

Friday, May 15, 2020 8:19 AM

A Sine function given by
,

[where
which is a sinusoidal graph with amplitude of
Remarks:

(a)
(b)
(c) Phase shift

 In general,

 Basic Graph
,

Phase shift

5.5 Trigonometric Functions Page 2

Cosine Function,

Friday, May 15, 2020 8:19 AM

A Cosine function given by
,

[where
which is also a sinusoidal graph with amplitude of

Remarks:
(a)
(b)

(c) Phase shift

 In general,

 Basic Graph
,

Phase shift

5.5 Trigonometric Functions Page 3

Tangent Function,

Friday, May 15, 2020 8:19 AM

A Tangent function given by
,

[where
which is a periodic curve with vertical asymptotes

Remarks: where
(a) Vertical asymptotes
(b)

(c) Phase shift

 In general,

 Basic Graph
,

Vertical asymptotes:

[This graph have 2 periods within it]

Phase shift

5.5 Trigonometric Functions Page 4

Example 10 & 11

Tuesday, June 30, 2020 4:01 PM

Example 10

Graph one period of the function .
State the domain and range of the function.

Solutions : https://www.geogebra.org/graphing/jmfspjtx

Amplitude= 5

Example 11

Sketch the graph of for .

State the domain and range of the function.

Solutions : https://www.geogebra.org/graphing/nfqd4wpq

Vertical asymptotes :

5.5 Trigonometric Functions Page 5