The sine function

Sine Function Sin 0° Sin π/2 Sin π Sin 3π/2 Sin 2π 1 π 3π/2 π/2 2π -1

Sine Function Domain: all reals Range: [-1, 1] Period is 2π (length of one complete cycle) Symmetric with respect to the origin Odd function 2π -2π

Amplitude Half the distance between the maximum and minimum values of the function y= a sinx Amplitude = |a| If |a|>1 the curve stretches If |a|<1 the curve shrinks New range is between a and -a

Period y = a sin bθ, where b>0 and θ is in radians If b is the number of cycles in the interval 0 to 2π, then the period is found by Ex: How many cycles does y = ½ sin ½ θ have in the interval 0 to 2π? What are the amplitude and period of this function?

Example: Sketch one cycle of a sine curve with amplitude 2 and period 4π

Graphing on the Calculator Your calculator must be in RADIAN mode! Set your window to fit your amplitude (y max/min) and period (x max/min) For basic graphs from 0 to 2π Xmin=0 Xmax=2π Xscl=π/2 Ymin=-5 Ymax=5 Yscl=1

Graph each function y = sin 5x Y= -5 sin 2θ

Solve sine equations Use y1 and y2 and find the intersection Example: Solve from 0 to 2π -2 sin θ = 1.2

Assignment In the Advanced Algebra books Page 425 # 1-9 odd, 17-27 odd, 31-37 odd