1. Recognise, sketch and interpret graphs of trigonometric functions
Grade 8
Trigonometric graphs
Recognise, sketch and interpret graphs of trigonometric functions
If you have any questions regarding these resources or come across any errors, please contact

2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Recognise, sketch and interpret graphs of trigonometric functions
Grade 8
Prior Knowledge
Translations and reflections of functions
Finding solutions graphically
Duration
60 minutes
Resources
Print slides:
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Plotting trig graphs
Give students slide 17 and 18 printed. Students to find exact values in order to plot the 3 trig graphs. Discuss the difference between drawing and sketching. 10
Features of sine graph
Give students slide 19 printed. Using slide 6 discuss the features of a sine graph. Show using slide 7 how to use the graph to find solutions. 5
Features of cosine graph
Give students slide 20 printed. Using slide 8 discuss the features of a cosine graph. Show using slide 9 how to use the graph to find solutions.
Features of tan graph
Give students slide 21 printed. Using slide 10 discuss the features of a sine graph. Show using slide 11 how to use the graph to find solutions.
Reasoning
Using the questions on slide 12 ask students to consider their responses in pairs and then feedback.
Transformation of trig graphs
Give students slide 22 printed. Students to work in pairs to sort the cards into two sets, deciding for themselves the criteria for their sets. Then ask them to sort their largest set into two subsets. Then repeat this once more for their largest set. They will now have four sets of cards. Their criteria might be as simple as ‘Has a 2 in front’. Give out some blank paper. Each pair to write a description of each of their sets and add an equation of their own to each set. Discuss the criteria that students have come up with and translate them into mathematical language if necessary; for example, “they have a 3 in front” can become “a one-way stretch in the direction of the y-axis with scale factor 3”; “A number in the bracket with x” can become “a translation of in the direction of the x-axis”.
Give students slide 23. Need to decide which equation goes with which graph. When they have done this, they should label the x and y axes accordingly. Students could then generalise their work by sketching and labelling graphs such as y = a sin x and y = cos bx. 20
Recognise, sketch and interpret graphs of trig functions
in exam questions (from specimen papers)
Give students slide 24. This includes 2 exam questions related to objective. Students to use notes from lesson. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated.
Next Steps
Assessment
PLC/Reformed Specification/Target8/Algebra/Trigonometric Graphs

3. Key Vocabulary
Trigonometric Sine Cosine Tangent Asymptote Period

4. Plotting Trig Graphs What do you notice when the graphs get to 3600?
Can you describe the relationship between the graphs of Sine and Cosine?

5. Plotting Trig Graphs

6. The sine graph y = sin x y x
Every value of sine between -1 and 1 gives two angles between 0 ° and 360°
The sine graph is periodic, repeating every 360°
Between 180° and 360° the values of sine are negative
Between 0° and 180° the values of sine are positive

7. The sine graph y = sin x 1 30 ° and 150° y x
Use the sine graph to find the value of sin 90°.
Use the sine graph to find the angles between 0° and 360° with a sine of 0.5.
30 ° and 150° y x

8. The cosine graph y = cos x
Every value of cosine between -1 and 1 gives two angles between 0 ° and 360°
The cosine graph is periodic, repeating every 360°
Between 90° and 270° the values of cosine are negative

9. The cosine graph y = cos x-1
Use the cosine graph to find the value of cos 180°.
Use the cosine graph to find the angles between 0° and 360° with a cosine of 0.5.
60 ° and 300° y x

10. The tangent graph y = tan x
Every value of tangent gives two positive values between 0 ° and 360°
The tangent graph is periodic, repeating every 180°
There are asymptotes at 90° and 270° on the positive side of the graph between 0° and 360°
Asymptotes: these are lines the graph approaches but does not meet. Try finding tan 90° on your calculator.

11. The tangent graph y = tan x
Use the tangent graph to find the value of tan 45°
Write down the coordinates of the three x-intercepts between 0° and 360° (inclusive) on the graph of tan x 1
(0,0)
(180,0)
(360,0)

12. Problem Solving and Reasoning
Explain why there is only one solution to the equation cos x = -1 for values in the range How would you find a solution to the equation sinx = cos x? How could you use the cosine key on your calculator to calculate values for sin x?

13. Sorting Initially into 2 groups.
Then split larger group into 2 sub groups. Then the larger of the sub group to be split again (you will end up with 4 groups)
You must be able to define your sorting criteria.

14. Match the equations to the graph and label the axes appropriately.
Transformations
Match the equations to the graph and label the axes appropriately.

15. Exam Question – Specimen Papers

16. Exam Question – Specimen Papers

17. Plotting Trig Graphs What do you notice when the graphs get to 3600?
Can you describe the relationship between the graphs of Sine and Cosine?
Student Sheet 1

18. Plotting Trig Graphs
Student Sheet 2

19. The sine graph y = sin x
Use the sine graph to find the value of sin 90°.
Use the sine graph to find the angles between 0° and 360° with a sine of 0.5.
Student Sheet 3

20. The cosine graph y = cos x
Use the cosine graph to find the value of cos 180°.
Use the cosine graph to find the angles between 0° and 360° with a cosine of 0.5.
Student Sheet 4

21. The tangent graph y = tan x
Use the tangent graph to find the value of tan 45°
Write down the coordinates of the three x-intercepts between 0° and 360° (inclusive) on the graph of tan x
Student Sheet 5

22. Sorting
Student Sheet 6

23. Match the equations to the graph and label the axes appropriately.
Transformations
Match the equations to the graph and label the axes appropriately.
Student Sheet 7

24. Exam Question – Specimen Papers
Student Sheet 8