Honors Pre-Cal Mrs. Cortez

xy = sin(x) 00 π /6½ π /21 5 π /6½ π 0 7 π /6-½-½ 3 π /2 11 π /6-½-½ 2π2π 0

(0, 0) Basic Graph of Sine Function 1 cycle ↔ PERIOD (how far it goes before it repeats)= 2π

TThe domain is the set of all real numbers. TThe range consists of all real numbers from -1 to 1, inclusive. TThe sign function is an odd function, as the symmetry of the graph is through the origin TThe sine function is periodic, with period 2 π. TThe x-intercepts are …, -2 π, - π, 0, π, 2 π, 3 π, …; the y-intercept is 0.

Properties continued Now for the cosine graph

xy = cos(x) 01 π /3½ π /20 2 π /3- ½ π 4 π /3- ½ 3 π /2 0 5 π /3½ 2π2π 1

(0, 1)

TThe domain is the set of all real numbers. TThe range consists of all real numbers from -1 to 1, inclusive. TThe sign function is an even function, as the symmetry of the graph is with the y-axis. TThe sine function is periodic, with period 2 π.

 y = d + a sin (bx – c)  y = d + a cos (bx – c)