5.3 Part 1 Trig Graphs

A function is periodic if its values repeat in a cycle. Sin and Cos functions repeat their values in a regular fashion. Since C = 2pi, then P(x, y) is the same as the point determined by t + 2pi Their values are unchanged by the addition of any integer multiple of 2pi. It’s period is the smallest positive number p such that f(x + p) = f(x)

sin and cos have period 2pi (the distance between any 2 sets of repeating points is 2 pi)

Graph of sin t

Graph cos t

Transformations Vertical Shifts:  f(X) + c up ‘c’ units  f(x) – c down ‘c’ units EX Graph f(x) = 2 + sin x

Reflections y = -f(x) – Reflects over the x-axis EX graph g(x) = -cos x

Ex Graph: y = 3 - cosx XY

Sin and Cos curves: y = a sin kx and y = a cos kx Amplitude = It is the largest value that these functions attain. Period =

Vertical Stretch & Shrink y = cf(x) – If c > 1, STRETCH vertically by a factor of ‘c’ – If 0 < c < 1, SHRINK vertically by a factor of ‘c’ EX Graph y = 2sin x

Stretch and Shrinking of sin graph

EX Graph: y = -3cosx

EX Find period and amplitude y = sin 2xy = sin ½ x y = 2cos3xy = -5sin1/3 x

5-Point Graphing XY

Ex Graph: y = sin2x XY

Ex Graph: y = ½ cos2x XY

Remember Sin x --- 0, max, 0, min, 0 Cos x --- max, 0, min, 0, max

pg 429 #1-25 odd