1. The 4 quadrants
90
2nd quadrant
1st quadrant 0
180
360
3rd quadrant
4th quadrant
270

2. Representing Angles 45° Measure from + x-axis
Anti Clockwise Direction for +ve angles
CW Direction for –ve angles

3. Representing Angles 45° −45° Measure from + x-axis
Anti Clockwise Direction for +ve angles
CW Direction for –ve angles

4. Representing Angles 135° −135° Measure from + x-axis
Anti Clockwise Direction for +ve angles
CW Direction for –ve angles

5. Representing Angles 225° −225° Measure from + x-axis
Anti Clockwise Direction for +ve angles
CW Direction for –ve angles

6. Special Angles 2 1 Equilateral Δ - equal lengths - equal angles 30
60 1
Assume each length is 2 units,
look at half of the Δ.

7. Special Angles
60
30 1 2

8. Special Angles 1 1 isosceles Δ - equal arms - equal base angles 45
Assume each arm is 1 unit.

9. The 4 quadrants 90 2nd quadrant 1st quadrant 0 180 360
sin +
cos −
tan −
sin +
cos +
tan + 0
180
360
sin −
cos −
tan +
sin −
cos +
tan −
3rd quadrant
4th quadrant
270

10. S sin + A all + T tan + C cos + The 4 quadrants 90 2nd quadrant
1st quadrant
S sin +
A all + 0
180
360
T tan +
C cos +
3rd quadrant
4th quadrant
270

11. 1st quadrant
90 1 2 0
30°

12. 2nd quadrant
90 2 1
30°
180

13. 3rd quadrant
180
30° −1 2
270

14. 4th quadrant
360
30° −1 2
270

15. Example 1
60° 1 2
Step 1: Find the unknown length and determine sin 60° and tan 60 °
240°
B.A = 60°
Step 2: Find the basic angle for 240° and determine the quadrant its in.

16. Example 2
45° 1
Step 1: Find the unknown length and determine sin 45° and cos 45 °
315°
B.A = 45°
Step 2: Find the basic angle for 315° and determine the quadrant its in.

17. Exercise Q1

18. Exercise Q2

19. Find the angles between 0 and 360 inclusive which satisfy
sin x =
Answer:
sin x =
basic angle = 47.94
 x = 47.9 or x = 180 
= 
or 

20. Find the angles between 0 and 360 inclusive which satisfy
tan x = −1.37
Answer: (1st step: find B.A for tan x = 1.37)
basic angle = 53.87
x = 180 − 53.87 = 
or x = 360 − 53.87 = 
 x = 126.1 or 

21. Find the angles between 0 and 360 inclusive which satisfy
cos (x − 27) = − 0.145
Answer:
0 < x < 360
− 27 < x − 27 < 333
basic angle = 81.66
x − 27 = 180 − 81.66 = 98.34  x = 
or x − 27 = 180  =   x = 
 x = 125.3 or 