Download The CAST Diagram

C2
The CAST Diagram
Objective: To be able to use the
CAST Diagram to determine
alternative trigonometric values.
Find the sine, cosine and tangent of each of these angles. Record the results in a table.
θ
30˚
60˚
120˚
150˚
210˚
240˚
300˚
330˚
sin θ
cos θ
tan θ
S C T
+
90˚
sin 120° =
3
2
sin 60° =
S C T
+
3
2
sin 30° = 0.5
sin 150° = 0.5
180˚
0˚
360˚
sin 210° = - 0.5
sin 330° = - 0.5
S C T
-
sin 240° = -
3
2
sin 300° = 270˚
3
2
S C T
-
90˚
S C T
+ -
cos 60° = 0.5
cos 120° = - 0.5
cos 150° = -
3
3
2
cos 30° = 2
0˚
360˚
180˚
cos 210° = S C T
- -
S C T
+ +
3
2
cos 330° =
cos 300° = 0.5
cos 240° = - 0.5
270˚
3
2
S C T
- +
90˚
S C T
+ - -
tan 120° = -
tan 150° = -
tan 60° =
3
1
S C T
+ + +
3
tan 30° =
3
3
0˚
360˚
180˚
tan 210° =
S C T
- - +
1
1
tan 330° = -
3
tan 240° =
tan 300° = -
3
270˚
3
1
3
S C T
- + -
90˚
S C T
+ - SSine positive
2nd
Quadrant
1st
S C T
+ + +
All positive
A
Quadrant
0˚
360˚
180˚
3rd Quadrant 4th Quadrant
TTangent positive
S C T
- - +
Cosine positive
C
270˚
The CAST Diagram
S C T
- + -
Some Observations:
•
The signs of the trigonometric ratios relate to the CAST diagram.
•
The magnitude of the trigonometric ratios are the same when reflected in the 90˚270˚ line, or in the 0˚-180˚ line.
•
The magnitudes of the sine and cosine of an angle when reflected in the 45˚-225˚
line or 135˚-315˚ line are swapped around. (sin becomes cos and vice versa)
1
The magnitude of tan becomes
when reflected in the 45˚-225˚ line or the 135˚tan
315˚ line
•
Example
Obtain exact values of the following trig ratios:
(i) cos 120°
(ii) sin 210°
(iii) tan 240°
(iv) cos 345°
(v) cos 150°
(vi) tan 270°
(vii) sin 315°
Example
Given cos  =
3
and that  is acute find exact values of:
5
(i) sin 
(ii) tan 
(iii) cos (180 + )
(iv) tan (90 + )
(v) sin (270 - )
(vi) cos (360 - )
Example
Given that  lies between 0° and 360° and that tan = - 3 indicate possible values of 
on separate diagrams. State the possible values of .