TRIGONOMETRIC GRAPHS

SINE GRAPHS The trig function “Sine” can be sketched Example 1: a) Complete the table of y = sinx for x [0°; 360°] 0° 30° 45° 60° 90° 120° 135° 150° 180° y = sin x 210° 225° 240° 270° 300° 315° 330° 360° y = sin x

Link between sinx as a ratio and as a graph

b) Determine the following based on the graph: The maximum value is…. 1 The minimum value is … -1 Amplitude = (maximum - minimum value) divided by 2 = (1-(-1)) 2 = 2 2 =1 c) Determine: The domain of the graph is … The range of the graph is …

Example 2: a) Draw the graph of y = sin x for x [-360°; 360°] b) After how many degrees does the graph (pattern) start repeating itself? … 360° This is called the period of the graph.

Exercise Graph Amplitude Maximum Minimum Period y = sin x y = 2 sin x y =3 sin x y = - sin x y = - 2 sin x The effects of a in y = asinx Amplitude shifts of y = asinx

Exercise Graph Amplitude Maximum Minimum Period y = sin x y = sin x + 1 y = sin x - 2 Vertical shifts of y = sinx + q

COS GRAPHS The trig function “Cosine” can be sketched Example 1: a) Complete the table of y = cosx for x [0°; 360°] 0° 30° 45° 60° 90° 120° 135° 150° 180° y = cos x 210° 225° 240° 270° 300° 315° 330° 360° y = cos x

Link between cosx as a ratio and as a graph

b) Determine the following based on the graph: The maximum value is…. 1 The minimum value is … -1 Amplitude = (maximum - minimum value) divided by 2 = (1-(-1)) 2 = 2 2 =1 c) Determine: The domain of the graph is … The range of the graph is …

Example a) Draw the graph of y = cosx for x [-360°; 360°] b) After how many degrees does the graph (pattern) start repeating itself? … 360° This is called the period of the graph.

Exercise Graph Amplitude Maximum Minimum Period y = cos x y= 2 cos x y = - 2 scos x

Exercise Graph Amplitude Maximum Minimum Period y = cos x

TAN GRAPHS The trig function “Tangent” can be sketched Example 1: a) Complete the table of y = tan x for x [0°; 360°] x is undefined at 90◦ and 270◦ Therefore, the tan graph has ASYMPTOTES at x = 90◦ and x = 270◦ 0° 45° 90° 135° 180° y = tan x 225° 270° 315° 360° y = tan x

b) Determine the following based on the graph: The maximum value is…. There is none! The minimum value is … There is none! Amplitude - There is none! However: y = atanx … a is the “amplitude” c) Determine: The domain of the graph is … The range of the graph is …

Example a) Draw the graph of y = tan x for x [-360°; 360°] b) After how many degrees does the graph (pattern) start repeating itself? … 180° This is called the period of the graph.

Exercise Graph Amplitude Maximum Minimum Period y = tan x y= 2 tan x

Exercise Graph Amplitude Maximum Minimum Period y = tan x