Trig Graphs The CAST diagram 16 September 2020

Trig Graphs & The CAST diagram 16 September 2020

The graph of y 1 0. 5 0 -0. 5 -1 180 360 x

The graph of y 1 0. 5 0 -0. 5 -1 100 200 300 x

The graph of y 20 10 0 -10 -20 180 360 x

The CAST Diagram Sin only positive 2 nd Quadrant 3 rd Tan only positive 1 st Quadrant 4 th Quadrant On the CAST diagram All angles are measured Anti-Clockwise All positive Cos only positive

y From the graph we can see that there are two solutions 1 On the CAST diagram there are two possible angles. One acute the other obtuse. 0. 5 0 A S 30° T C x = 150° T -1 C x = 30° -0. 5 180 360 x

y 20 From the graph we can see that there are two solutions 10 On the CAST diagram there are two possible angles. One reflex the other obtuse. 0 180 360 -10 A S -20 60° T C x = 120° T 60° C x = 300° On the CAST diagram A negative angle means we move Clockwise x

(i) A S 41. 8° T C x = 138. 2° A S T C x = 41. 8°

(ii) A S 75. 5° T C T x = 284. 5° C x = 75. 5° (iii) A S 33. 7° T C x = 146. 3° A S T 33. 7° C x = 326. 3°

A S 45° T C x = 315° x = 45° (i) S A 135° T C x = 135° A S T 135° x = 225° C

Trig Equations 1. Solve each of the following equations in the range of 0º to 360º a) b) c)

d) e) f)

g) 2. Solve the equation in the range 0º to 360º