features of 6 trig parent functions

Question 1

y=sin(x)

Answer 1

Graph: “starts” at the origin, looks like the waves
Domain: all real numbers
Range: [-1,1]
Period: 2pi

Question 2

y=cos(x)

Answer 2

Graph: “starts” on the y-axis, looks like a valley
Domain: all real numbers
Range: [-1,1]
Period: 2pi

Question 3

y=tan(x)

Answer 3

Graph: increasing squiggle line, crosses through the origin
Domain: all real numbers, x cannot equal pi/2 + npi
Range: (negative infinity, positive infinity)
Period: pi

Question 4

y=cot(x)

Answer 4

Reciprocal of tangent
Graph: decreasing squiggle line, y-axis is an asymptote
Domain: all real numbers, x cannot equal npi
Range: (negative infinity, positive infinity)
Period: pi

Question 5

y=csc(x)

Answer 5

Reciprocal of sine
Graph: the u’s with the y-axis as the asymptote
Domain: all real numbers, x cannot equal npi
Range: (negative infinity, negative 1] U [1, positive infinity)
Period: 2pi

Question 6

y=sec(x)

Answer 6

Reciprocal of cosine
Graph: the u’s with one that intercepts the y-axis
Domain: all real numbers, x cannot equal pi/2 + npi
Range: (negative infinity, -1] U [1, positive infinity)
Period: 2pi