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# How to draw a Sine function?

### Sine function example 1 (five points method)

### Sine function example 2 (the amplitude determined by ?)

### Sine function example 3 (the period determined by ?)

### Sine function example 4 (the symmetry of Sine function)

### Sine function example 5 (Phase Shift : Right Shift)

### Sine function example 6 (Phase Shift : Left Shift)

### Sine function example 7 (property)

- Graphic of y = sin x

- The five key points in one period of sin x is:
- (0 , 0), (pi/2 , 1) (pi , 0), (3pi/2, -1), (2pi, 0)
- Its maximum value is 1 and the minimum value is -1 and period is 2pi.

- The amplitude of y = A sin x is the largest value of y and is given by
- amplitude = |A|
- Amplitude determines vertical stretch or shrink.

- The period of y = A sin Bx is 2pi/B, in which B is a positive number.
- For y = sin x, A = 1, B = 1, period = 2pi/B = 2pi/1 = 2pi
- For y = sin 2x, A = 1, B = 2, period = 2pi/B = 2pi/2 = pi
- For y = sin (1/2)x, A = 1, B = 1/2, period = 2pi/B = 2pi/(1/2) = 4pi

- The sine graph is symmetric with respect to the origin.
- y = sin x is a odd function
- sin(-x) = - sin x
- sin x is a period function, sin x = sin(x + 2 pi n), n = 0, 1, 2, 3..., -1, -2, -3...,

- The graph of y = sin(x - pi/4) is the graph of y = sin x right shift pi/4

- The graph of y = sin(x + pi/4) is the graph of y = sin x left shift pi/4

- The properties of Sine function y = A sin( Bx - C ), in which B > 0 are:
- amplitude = |A|
- period = 2pi/B
- The phase shift and resulting interval for a period are solutions to the equations
- Bx - C = 0 and Bx - C = 2pi

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