ch10 graphing trigonometric functions

Question 1

what’s a periodic function?

Answer 1

a function whose value repeats at constant intervals. the length of this function is called a period.

Question 2

how do you graph y=sin(x)?

Answer 2

middle, up, middle, down.

Question 3

how do you graph y=cos(x)?

Answer 3

up, middle, down, middle.

Question 4

how do you graph y=csc(x)?

Answer 4

graph sin first, then make asymptotes at “middle” values.

Question 5

how do you graph y=sec(x)?

Answer 5

graph cos first, then make asymptotes at “middle” values.

Question 6

what are the periods of sin, cos, csc, and sec?

Answer 6

2pi

Question 7

what are the x values of sin, cos, csc, and sec?

Answer 7

0, pi/2, pi, 3pi/2, 2pi.

Question 8

how do you graph y=tan(x)?

Answer 8

down, middle, up.

Question 9

how do you graph y=cot(x)?

Answer 9

up, middle, down.

Question 10

what are the periods of tan and cot?

Answer 10

pi

Question 11

what are the x values of tan and cot?

Answer 11

-pi/2, -pi/4, 0, pi/4, pi/2.

Question 12

y=2tan(x)

Answer 12

tan with a vertical stretch of 2

Question 13

y=sin(x)+3

Answer 13

sin, up 3

Question 14

y=cos(2x)

Answer 14

cos with a horizontal shrink of 2

Question 15

y=sin(x-pi/3)

Answer 15

sin, right pi/3

Question 16

write “y=3cos(2x-2pi)-1” in standard form.

Answer 16

y=3cos2(x-pi)-1

Question 17

rewrite “y=2-4csc(x/2-pi)” in standard form.

Answer 17

y=-4csc1/2(x-2pi)+2