sketching trigonometric graphs - firrhill high...

Sketching Trigonometric Graphs

Starter

1) True or false? cos (x) = 1 + sin (x)

Why?

2) Solve 1 + 4sin(x) = 3 for 0 < x < 360

2 2


Today we are learning...

How to sketch a variety of trigonometric graphs.

I will know if I have been successful if...

I can complete a table of values using a calculator.

I can plot the points from the table of values.

I can state the period and amplitude of a curve.


Plotting y = sin(x)

x 0 45 90 135 180 225 270 315 360

y

1) Complete the table of values.

Round your values to 2 decimal places.

Plotting y = sin(x)

x 0 45 90 135 180 225 270 315 360

y 0 0.71 1 0.71 0 -0.71 -1 -0.71 0

1) Complete the table of values.

Round your values to 2 decimal places.


2) Plotting the points from the table.

1

-1

x 0 45 90 135 180 225 270 315 360

y 0 0.71 1 0.71 0 -0.71 -1 -0.71 0

y = sin(x)

3) State the amplitude and period.

1

-1

Amplitude = 1 Period = 360 o

y = sin(x)



1) I can complete a table of values using a calculator.

2) I can plot the points from the table of values.

3) I can state the period and amplitude of a curve.

Checklist

Desmos

Let's check our answers using desmos....

1) y = cos(x)

2) y = tan(x)

Challenge

3) y = 2sin(x)

4) y = sin(2x)

5) y = 3cos(4x) - 1


Summary

You are going to see 5 trigonometric graphs.

For each one on your whiteboard write down the...

Period =

Amplitude =

Summary

State the period and amplitude of each curve.1.


Summary


Period = 120o

Am

plitude = 3

Summary



Summary


Period = 180 o

Am

plitude = 3

Summary



Summary


Period = 90 o Amplitude = 0.5

Summary



Summary


Period = 60o

Am

plitude = 5

Summary



Summary


Period =

40o

Am

plitude = 2



How to sketch a variety of trigonometric graphs.


I can complete a table of values using a calculator.

I can plot the points from the table of values.



Transformations of Trigonometric Graphs


How to transform graphs to change their amplitude and period.



I can find a link between the equation of the curve and the amplitude and period.

I can sketch a trigonometric curve without the aid of a table of values.

Equation Amplitude Period

y = sin(x)

y = cos(x)

Investigation


y = 3cos(3x)


Period = 120o

Am

plitude = 3

y = 3sin(2x)


Period = 180 o

Am

plitude = 3


y = 0.5sin(4x)


Period = 90 o Amplitude = 0.5

y = 5cos(6x)


Period = 60o

Am

plitude = 5


y = 2cos(9x)


Period =

40o

Am

plitude = 2

Equation Amplitude Period

y = sin(x) 1 360

y = cos(x) 1 360

y = 3cos(3x) 3 120

y = 3sin(2x) 2 180

y = 0.5sin(4x) 0.5 90

y = 5cos(6x) 5 60

y = 2cos(9x) 2 40

Investigation


Conclusion

The graphs of y = acos(bx) and y = asin(bx)...

have amplitude a

and a period of

y = asin(x) always starts at the origin.

360b

o

Example 1

Sketch y = 2sin(x)


Example 2

Sketch y = 1.5cos(x)

Practice

Choosing a suitable scale, sketch the following trigonometric graphs without using a table of values.

a) y = 3cos(x)

b) y = 2sin(x)

c) y = 0.5sin(x)

d) y = -4cos(x)

Challenge

e) y = 2.25sin(2x)


Summary

Match the trigonometric equations with the graphs.

Log onto desmos...

1) y = 3cos(x)

2) y = 3sin(2x)

3) y = 2sin(2x)

Starter

1) Find the period and amplitude of the following

a) y = 3cos(4x)

b) y = tan(x)

c) y = -5sin(9x)

2) Find the roots of the graph y = x + 5x - 242


Graphing Trigonometric Functions


How to sketch trig functions without drawing a table.


I know where the curve starts.

I know the period and amplitude of the curve.

I can sketch the graph.

y = 2cos(3x) - Amplitude

- Period

- Origin?


y = 3sin(6x) - Amplitude

- Period

- Origin?

Practice

1) y = 2cos(3x)

2) y = 4cos(2x)

3) y = sin(6x)

4) y = 3cos(12x)

5) y = -2sin(3x)

6) y = 4cos(6x)

Check answers on desmos...


National 5 Exam Questions

National 5 Exam Questions


Graphing Trigonometric Functions


How to sketch trig functions without drawing a table.


I know where the curve starts.

I know the period and amplitude of the curve.

I can sketch the graph.

sketching trigonometric graphs - firrhill high...

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