1. The sine function

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

3. 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

4. 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

5. 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?

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

7. 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

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

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

10. Assignment In the Advanced Algebra books
Page 425 # 1-9 odd, odd, odd