2. Presents Mathematics Department

3. Graphs of Sine, Cosine and Tangent The combined graphs Summary Solving trigonometric equations Menu

4. Graphs

7. What about tan 70°? tan 80°? tan 85°? Can you explain whats happening?

8. Sin xº 0 1 90 360 270180 xº Graph of Sin x°

9. Cos xº Graph of Cos x° 0 1 90 360 270180 xº

10. Tan xº Graph of Tan x° 0 1 90 360 270180 xº This isnt drawn to scale- but it looks something like this!

11. 0 - 90° Sin x ° +ve Cos x ° +ve Tan x ° +ve Combined Graphs 0 1 90 360 270180 xº Sin xº Cos xº Tan xº

12. Sin x ° +ve Cos x ° -ve Tan x ° -ve Combined Graphs 0 1 90 360 270180 xº Sin xº Cos xº Tan xº 90°-180°

13. Sin x ° -ve Cos x ° -ve Tan x ° +ve Combined Graphs 0 1 90 360 270180 xº Sin xº Cos xº Tan xº 180°-270°

14. Sin x ° -ve Cos x ° +ve Tan x ° -ve Combined Graphs 0 1 90 360 270180 xº Sin xº Cos xº Tan xº 270°-360°

15. 270° 180° 90° 0°0° Summary

16. 270° 180° 90° 0°0° Sin x ° +ve Cos x ° +ve Tan x ° +ve Sin x ° +ve Cos x ° -ve Tan x ° -ve Sin x ° -ve Cos x ° -ve Tan x ° +ve Sin x ° -ve Cos x ° +ve Tan x ° -ve SinTanCosAll Which are positive? Summary

17. 270° 180° 90° 0°0° Sin x ° +ve Cos x ° +ve Tan x ° +ve Sin x ° +ve Cos x ° -ve Tan x ° -ve Sin x ° -ve Cos x ° -ve Tan x ° +ve Sin x ° -ve Cos x ° +ve Tan x ° -ve Sinners TakeCare! All Which are positive? Summary

18. Cos x° = 0.50 x360 Cos xº 0 1 90360270180 xº 0.5 60°300° Example 1 So x = 60°, 300°

19. 270° 180° 90° 0°0° Cos x° = 0.50x360 A T S C (Cos ¹ 0.5 = 60°) 300° x = 60°, 300° Example 2 60° Cos +ve

20. 270° 180° 90° 0°0° Sin x° = -0.50x360 A T S C 30° Sin -ve (Sin ¹ 0.5 = 30°) Sin -ve, 330°x = 210° 30° Example 3

21. 270° 180° 90° 0°0° 2Sin x° = 10x360 A T S C (Sin ¹ ½ = 30°) x = 30° Sin x° = ½,150° 30º Example 4 Sin +ve

22. 270° 180° 90° 0°0° 3 cos x° = -1 0x360 A T S C cos -ve (cos ¹ = 70.5°) cos -ve, 250.5°x = 109.5° 3 cos x°+1 = 0 cos x° = - 70.5° Example 5

23. Mathematics Department