# Math Investigation - Sine Law

Part 1

Look at the graphs of y = sin x

Compare the graphs of:

y = sin x

y = 2sin x

y = 1/3sin x

y = 5sin x

The difference between all these graphs is a variable known as A, or amplitude of wave.

When A > 1, the graph stretches vertically.

When 0 < A < 1, the graph compresses vertically.

Also, A is the number that manipulates how far the graph compresses or stretches to. For example, in the graph of y = 2sin x, the graph stretches out to +2 and down to -2. The characteristics of the waveform are altered because of this. The range of the graph is increased or decreased in conclusion.

The domain and range of the graphs are:

y = sin x

D: {x| xεR}

R: {y| -1 < y < 1, yεR}

y = 2sin x

D: {x| xεR}

R: {y| -2 < y < 2, yεR}

y = 1/3sin x

D: {x| xεR}

R: {y| -1/3 < y < 1/3, yεR}

y = 5sin x

D: {x| xεR}

R: {y| -5 < y < 5, yεR}

Also, if A was negative in the initial equation, it would flip the graph around like a mirror as so:

y = 2sin x

y = -2sin x

Part 2

Investigate the family of curves y = sin (x + C), where 0o ≤ C ≤ 360o. How does the value of C transform the standard curve y = ...