Graphing trig functions

sin y = asin(b(x + c)) + d

cosine y = acos(b(x+c)) + d

tan y = atan(b(x + c)) + d

cot y = acot(b(x + c)) + d

a = the amplitude of the function = |a| = max-min/2 the distance from the midline to top or bottom of the graph

in tangent, cosecant, secant, and cotangent, the amplitude is inf

b = the period of the function = 2pi/|b| for sin,cos,sec,csc and pi/|b| for tan,cot how long it takes for the function to complete a rotation and restart

c = horizontal shifts. positive c shifts the function to the left (subtract c from each x value) and negative c shifts to the right

d = vertical shifts. positive d shifts upward (add d to each y value) and negative shifts down

Combinations

Ex: graph y = sinx + cos(2x)

Graph both functions independently and then use them to visualize and graph points of the combination

Finding points where the values are close together is the best