The CAST diagram
Sin only
positive
2nd
Quadrant
3rd
Tan only
positive
1st
All positive
Quadrant
4th
Quadrant Quadrant
Cos only
positive
Example
Obtain exact values of the following trig ratios:
(i)
Cos 120°
(ii)
Tan 240°
(iii) Cos 150°
(iv) Sin 315°
Cos 120°
A
S
120
60°
T
C
Cos 120° = – cos 60
= –
Tan 240°
A
S
240
60°
T
C
Tan240° = Tan 60
 3
Cos 150°
A
S
150
30°
T
C
Cos 150° = – cos 30
3

2
Sin 315°
A
S
315
45°
T
C
sin315° = – Sin 45

1
2
Example
Given cos =
(i)
Sin
(ii)
tan
3
and that  is acute find exact values of
5
(iii) Cos(180+)
(iv) Tan(90+)
(v) Sin(270 – )
(vi) Cos(360 – )
cos  
3
5
5
4

3
4
(i) sin  
5
(ii) tan  
4
3
Cos(180+)
A
S
180+

T
C
Cos(180+) = – cos 
3

5
Tan(90+)
A
S
90+
90 - 
T
C
Tan(90+) = –
90 - 
5
4

3
Tan(90–)
3

4
Sin(270 – )
A
S
270-
90-
T
C
Sin(270 – ) = – Sin(90 – )
3

5
Cos(360 – )
A
S
360-

T
C
Cos(360 – ) = cos 
3

5
Example
Given that  lies between 0° and 360° and that
tan = - 3 indicate possible values of  on separate
diagrams. State the possible values of .
A
S
A
S
60°
60°
T
C
 = 120°
T
C
 = 300°