Section+4.4


 * Section 4.4: Graphs of Sine and Cosine: Sinusoids**


 * Homework**

//pg. 392 (1-27) odd & pg. 393 (61-68)//


 * Graphs of Sine and Cosine**

y = sin(x)

y = cos(x)


 * Periodic Functions**

__periodic function__- a function y = f(x) is periodic if there is a positive number 'c' such that f(t+c) = f(t) for all values of 't' in the domain of f. The smallest such number 'c' is called the period of the function. y = sin(x) -- period is 2π y = cos(x) -- period is 2π


 * Sinusoids**

__sinusoid__- a function is a sinusoid if it can be written in the form: f(x) = a*sin[b(x-c)] + d a,b,c,d are constants (neither a nor b can be zero) new period = old period / |b| frequency = |b| / old period (the number of complete cycles the wave completes in a unit interval)
 * a| = amplitude (half the height of the wave)
 * Examples**

//y = 1/2cos(x + π/2)// amplitude: 1/2 period: 2//π// phase shift: left π/2

//y = sin(2x + 6)// = sin[2(x + 3)] (factor out 2 to ensure that x has a coefficient of 1) amplitude: 1 period: π phase shift: left 3

//Write the cosine function as a phase shift of the sine function:// y = sine(x + π/2)

//Create a sinusoid with period π/5 and amplitude 6 which goes through (2,0):// y = a*sin[b(x-c)] + d new period: π/5 = 2π/b b = 10 phase shift: right 2 final answer: y = 6sin[10(x-2)]