10.3 Graphs of `y` = `a` sin( `bx` + `c`) and `y` = `a` cos(`bx` + `c`)

Phase Angle • Displacement • Graphs of $y = a \sin (b x + c)$ and $y = a \cos (b x + c)$ • Cycle

In the function $y = a \sin (b x + c),$ c represents the phase angle. It is another very important quantity in graphing the sine and cosine functions. Its meaning is illustrated in the following example.

EXAMPLE 1 Sketch function with phase angle

Sketch the graph of $y = \sin (2 x + \frac{π}{4}) .$

Here, $c = π / 4 .$ Therefore, in order to obtain values for the table, we assume a value for x, multiply it by 2, add $π / 4$ to this value, and then find the sine of the result. The values shown are those for which $2 x + π / 4 = 0, π / 4, π,$ 2, $3 π / 4, π,$ and so on, which are the important values for $y = sin ...$

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans

10.3 Graphs of `y` = `a` sin( `bx` + `c`) and `y` = `a` cos(`bx` + `c`)

EXAMPLE 1 Sketch function with phase angle

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