Trigonometric Graphs Y sinx 1 0 90 180

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Trigonometric Graphs

Y = sinx 1 0 90 180 -1 Maximum Value = 1 Minimum Value = -1 270 360

Y = cosx 1 0 90 180 -1 Maximum Value = 1 Minimum Value = -1 270 360

Y = 7 sinx →range = 14 7 0 90 180 Range 270 360 -7 Maximum Value = 7 Minimum Value = -7 Range = Max - Min Range = 7 – (-7) = 14

4 0 Y = 4 cosx 90 →range = 8 180 -4 Maximum Value = 4 Minimum Value = -4 270 360

Y = -8 sinx 8 0 90 180 -8 “Opposite” to Sin x Maximum Value = 8 Minimum Value = -8 270 360

Y = sin x 1 0 90 180 270 360 450 -1 Cycle starts again Period of graph is 3600 Between 00 and 3600 there is 1 cycle Also applies to Y = cos x 540

Y = sin 2 x 1 0 90 180 270 360 -1 Period of graph is 1800 There are 2 cycles between 00 and 3600

Combining these rules Draw y = 6 sin 2 x Max 6 2 cycles Min -6 Period = 360 ÷ 2 = 1800 6 0 -6 Y = 6 sin 2 x 90 180 270 360

Recognising Graph Max 8 4 cycles Cosine Min -8 Y = 8 cos 4 x 8 0 -8 90 180 270 360

Remember rules for y = (x-3)2 + 5 3 units to right Same rules for trig graphs! Up 5

3 2 Y = sinx + 2 1 Y = sinx 0 -1 90 180 270 360

Y = 4 cos (x – 450) 4 0 90 -4 Y = 4 cosx 180 270 360 450

Goes to infinity What about y = Tanx ? ? ? 0 90 Period is 1800 180 270 360 Cycle complete No Maximum (or minimum)

12 8 range = 8 4 Graph Type 0 90 180 270 y = 4 cosx 360 -4 Y = 4 cosx + 6