AS Maths Masterclass

1. AS Maths Masterclass Lesson 2: Trigonometrical equations

2. Learning objectives The student should be able to: • derive standard results for sin, cos, tan of 30, 45 and 60 degrees respectively; • define the sin, cos and tan functions and sketch their graphs; • apply the identity when appropriate; • apply the Pythagorean identity when appropriate.

3. What is trigonometry and where is it used? It is all about how the sides and angles of a triangle are related to each other. You are about to see a number of images. Identify the role played by trigonometry in each case:

4. The sundial

5. The speedcam

6. The pyramids

7. A map (showing what ?)

8. A tuning fork

9. The humble bumble bee

10. A plug for your electrical gadgets

11. Every student’s essential kit

12. A metronome

13. A spring

14. Defining the trig functions You are about to visit an interactive spreadsheet. Notice the colour code for each trig function and the graphs they produce. Click here to move to the Excel spreadsheet

15. Key features of sin x graph • Periodic with period 360 degrees. • Rotational symmetry order 2 about origin. • Vertical lines of symmetry at 90, 270 etc. • Maximum value = 1 • Minimum value = -1

16. Key features of cos x graph • Periodic with period 360 degrees. • Reflective symmetry in the y axis. • Vertical lines of symmetry at 0, 180, 360 etc. • Maximum value = 1 • Minimum value = -1

17. Key features of tan x graph • Periodic with period 180 degrees. • Rotational symmetry of order 2. • Vertical lines of symmetry at 0, 180, 360 etc. • Maximum value = • Minimum value = -

18. Derivation of standard results Click here for weblink 1: 30, 45, 60 deg. Click here for the Excel spreadsheet Click here for the weblink list.