Unit 3 - Unit Circle and Trig Graphs

unit circle: angles corresponding with 45 degrees and their radian measures

45 is pi/4 and increase by pi/4 for each increase by 45

unit circle: angles corresponding with 30 degrees and their radian measures

30 is pi/6 and increase by pi/6 for each increase by 30

unit circle: coordinates of 45

(root 2/2, root 2/2) with sign changes

unit circle: coordinates of 30

(root 3/2, 1/2) with sign changes

unit circle: coordinates of 60

(1/2, root 3/2) with sign changes

unit circle: cos

x coordinate

unit circle: sin

y coordinate

unit circle: tan

y coordinate/x coordinate

period for sin and cos

2π/b

sin graph

starts and ends at midline, at amp at pi/2, back at midline at pi, at -amp at 3 pi/2, ends at 2 pi

cos graph

starts and ends at peak, at midline at pi/2, at -amp at pi, back at mid at 3 pi/2, at peak at 2 pi

tan graph

0 at 0, 1 at pi/4, -1 at -pi/4, asymptotes at +- pi/2, period pi

cot graph

0 at pi/2, 1 at pi/4, -1 at 3pi/4, asymptotes at 0, pi, period pi

tan interval

+- pi/2b

cot interval

0, pi/b

csc graph

draw sin, draw reciprocal, asymptotes where sin line is at 0

sec graph

draw cos, draw reciprocal, asymptotes where cos line is at 0

odd function

-f(x) = f(-x), symmetric about origin, sin, tan, csc, cot

even function

f(x) = f(-x), symmetric over y axis, cos, sec

arc sin (sin^-1)

range of -pi/2, pi/2, switch normal sin coordinates

arc cos (cos^-1)

range of 0, pi,

equation meaning

y = a \* sin (bx - d) + c, a is amp, b is stretch/k, d is left right, c is midline