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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 .