Brain Growth Senior Phase - calderglen.s-lanark.sch.uk

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Extend and Succeed

Brain Growth ? Senior Phase

Trigonometry

Graphs and Equations

Trig Graphs

O1 Trig ratios of angles of all sizes

1.

Given the diagram above, find sin 130?, cos 130? and tan 130? correct to 2 significant figures. 2.

Given the diagram above, find sin 220?, cos 220? and tan 220? correct to 2 significant figures. Page | 2

3.

Given the diagram above, find sin 320?, cos 320? and tan 320? correct to 2 significant figures. 4.

Given the diagram above, find sin -60?, cos -60? and tan - 60? correct to 2 significant figures. Page | 3

O2

I can use ICT to plot and analyse Trig Graphs

1. (a) Set the following DOMAIN and step size on Desmos.

DOMAIN -60 420 STEP SIZE 30

(b) Set the following RANGE.

RANGE -2 2

STEP SIZE 0.5

(c) Use Desmos to plot = sin x?.

(d) Sketch and annotate the graph of = sin x? on worksheet 1.

(e) Write down the amplitude and period of the graph of = sin x?.

(f) Write down the coordinates of where your graph of = sin x? cuts the axes and the coordinates of all of the turning points.

2. (a) With the same DOMAIN and RANGE, use Desmos to plot = cos x?. (b) Sketch and annotate the graph of = cos x? on worksheet 1. (c) Write down the amplitude and period of the graph of = cos x?. (d) Write down the coordinates of where your graph of = cos x? cuts the axes and the coordinates of all of the turning points.

3. (a) Keep the same DOMAIN, but set the following RANGE.

RANGE -5 5

STEP SIZE 1

(b) Use Desmos to plot = tan x?.

(c) Sketch and annotate the graphs of = tan x? on worksheet 1

Page | 4

(a) Investigating the (peak) amplitude

4. Plot the graphs of the following using desmos and look for a connection between the equation and the amplitude.

You will have to adjust the RANGE so that the whole graph fits on the screen.

(a) = 2 sin x? (c) = 10cos x? (e) = 3sin x?

(b) = 5cos x? (d) = 5 sin x? (f) = 15cos x?

5. Plot the graphs of the following using desmos and look for a connection between the equation and the amplitude.

(a) = 2 sin x? + 1 (c) = 10cos x? + 3 (e) = 3sin x? + 1

(b) = 5cos x? - 1 (d) = 5 sin x? - 2 (f) = 15cos x? - 5

6. Predict the amplitude of graphs of each of the following and check your answer by plotting the graph.

(a) = 3 sin x? - 4 (c) = cos x? + 5 (e) = 5sin x? - 3

(b) = 2cos x? + 1 (d) = 4 sin x? - 1 (f) = 10cos x? + 9

Page | 5

(b) Investigating the vertical translation

7. Plot the graphs of the following using desmos and look for a connection between the equation and vertical translation.

(a) = sin x? + 1 (c) = cos x? + 3 (e) = sin x? + 1

(b) = cos x? - 1 (d) = sin x? - 2 (f) = cos x? - 5

8. Plot the graphs of the following using desmos and look for a connection between the equation and vertical translation.

(a) = 2 sin x? + 1 (c) = 10cos x? + 3 (e) = 3sin x? + 1

(b) = 5cos x? - 1 (d) = 5 sin x? - 2 (f) = 15cos x? - 5

9. Predict the vertical translation of the graphs of each of the following and check your answer by plotting the graph.

(a) = 3 sin x? - 4 (c) = cos x? + 5 (e) = 5sin x? - 3

(b) = 2cos x? + 1 (d) = 4 sin x? - 1 (f) = 10cos x? + 9

Page | 6

(c) Investigating the period

10. Plot the graphs of following using desmos and look for a connection between the equation and period.

(a) = sin 2x? (c) = cos 2x? (e) = sin 3x?

(b) = cos 3x? (d) = sin4 x? (f) = cos 4x?

11. Plot the graphs of following using desmos and look for a connection between the equation and the period.

(a) = sin 2x? + 1 (c) = cos2 x? + 3 (e) = sin 3x? + 1

(b) = cos 3x? - 1 (d) = sin4 x? - 2 (f) = cos 4x? - 5

12. Predict the period of graphs of each of the following and check your answer by plotting the graph.

(a) = sin3 x? - 4 (c) = cos5 x? + 1 (e) = 5sin3 x? - 3

(b) = cos2 x? + 1 (d) = 4 sin 2x? - 1 (f) = 10cos 4x? + 1

Page | 7

(d) Investigating the horizontal translation (phase angle)

13. Plot the graphs of following using desmos and look for a connection between the equation and the horizontal shift.

(a) = sin(x - 30)? (c) = cos(x - 90)? (e) = tan(x - 90)?

(b) = cos(x - 45?) (d) = tan( x - 45)? (f) = cos(x - 30)?

14. Plot the graphs of following using desmos and look for a connection between the equation and the horizontal shift.

(a) = sin(x + 30)? (c) = tan(x + 90)? (e) = sin(x + 90)?

(b) = cos(x + 45?) (d) = sin( x + 45)? (f) = tan(x + 30)?

15. Predict the horizontal shift of the graphs of each of the following and check your answer by plotting the graph.

(a) = 3 sin(x + 15)? (c) = tan(x - 30)? (e) = sin(x + 90)? + 2 (g) = 5sin(x - 30)? - 2 (i) = tan(x + 90)?

(b) = cos(x + 180?) - 1 (d) = 3sin( x + 45)? (f) = tan(x - 60)? (h) = 2cos(x + 15?) + 3 (j) = 4sin( x - 45)?

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