Week 11 - Trigonometry

Day 51
π
1. Quiz 6 Feedback 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π 2π
x

7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

2. Examples
Sketch the graph of y = −3cos ( x + π ) + 1

2. Examples

y = cos ( x )

2. Examples

y = −3cos ( x )

2. Examples

y = −3cos ( x + π )

2. Examples
y = −3cos ( x + π ) + 1

2. Examples
Sketch the graph of ( )
y = 2sin x − π 3 − 1

2. Examples
y = 2sin x − π 3 − 1

y = sin ( x )

2. Examples
y = 2sin x − π 3 − 1

y = 2sin ( x )

2. Examples
y = 2sin x − π 3 − 1

(
y = 2sin x − π 3 )

2. Examples
y = 2sin x − π 3 − 1

( )
y = 2sin x − π 3 − 1

2. Examples
Sketch the graph of y = 3cos ( 2x + π ) + 1

2. Examples
y = 2sin 2x − π 3 − 1

Day 52
1. Examples

Find the amplitude and period of y = 3 sin 4x and sketch the graph of
the function.

Day 52
1. Examples

the function.

If , the amplitude and period of
and are given by:

Day 52
1. Examples

the function.

If ω > 0 , the amplitude and period of
and are given by:

Day 52
1. Examples

the function.

If ω > 0 , the amplitude and period of y = Asin ω x
and are given by:

Day 52
1. Examples

the function.

and y = A cos ω x are given by:

Day 52
1. Examples

the function.


Amplitude =

Day 52
1. Examples

the function.


Amplitude = A

Day 52
1. Examples

the function.


Amplitude = A Period = T =

Day 52
1. Examples

the function.


2π
ω

1. Examples

the function.

2. Phase Shift

Find the amplitude and period of y = 3sin ( 2x − π ) and sketch the
graph of the function.

2. Phase Shift


If , for the graphs of
and are given by:

2. Phase Shift


If ω > 0 , for the graphs of
and are given by:

2. Phase Shift


If ω > 0 , for the graphs of y = Asin (ω x − φ )
and are given by:

2. Phase Shift


If ω y = Asin (ω x − φ )
> 0 , for the graphs of
and y = A cos (ω x − φ ) are given by:

2. Phase Shift



Amplitude =

2. Phase Shift



Amplitude = A

2. Phase Shift




2. Phase Shift



2π
ω

2. Phase Shift



2π
Amplitude = A Period = T = Phase shift =
ω

2. Phase Shift



2π φ
Amplitude = A Period = T = Phase shift =
ω ω

3. Classwork

Solve the given exercises.

4. Answers

( )
y = 3cos x − π 3 + 1

4. Answers

( )
y = −2sin x − π 2 − 1

4. Answers

( )
y = 3cos 2x − π 3 + 1

4. Answers

( )
y = −2sin 2x − π 3 − 1

Day 53
1. Homework check

y = sin x

1. Homework check

y = cos x

2. Graphs of Trigonometric Functions


y = sin x


y = sin x

y = cos x


y = sin x

y = cos x
sin x
y = tan x =
cos x


y = sin x

y = cos x
sin x
y = tan x =
cos x

y = tan x


y = sin x

y = cos x
cos x
y = cot x =
sin x


y = sin x

y = cos x
cos x
y = cot x =
sin x

y = cot x


y = sin x

y = cos x
1
y = sec x =
cos x


y = sin x

y = cos x
1
y = sec x =
cos x

y = sec x


y = sin x

y = cos x
1
y = csc x =
sin x


y = sin x

y = cos x
1
y = csc x =
sin x

y = csc x

Week 11 - Trigonometry

More Related Content

What's hot (20)

Viewers also liked (20)

Similar to Week 11 - Trigonometry (20)

More from Carlos Vázquez (20)

Recently uploaded (20)

Week 11 - Trigonometry

Editor's Notes