Question

1. ) The solid graph is the graph of one of the six main trigonometric functions. Which of the six is it? How do you know this?

Answer 1

any ideas on this at all?

Answer 2

no i dont

Answer 3

when x = 0, sin(x) is

sin(x) = sin(0) = 0

so when x = 0, sin(x) = 0 which rules out the sine function

Answer 4

because on this graph is the point (0,1)

Answer 5

when x = 0, cos(x) = ???

Answer 6

1?

Answer 7

so (0,1) is on the graph of cos(x)

so far so good

when x = pi/2, cos(x) = ???

Answer 8

is this from the unit circle?

Answer 9

yes

Answer 10

so is it 1?

Answer 11

cos(pi/2) is not 1

Answer 12

I dont know it

Answer 13

do you have the unit circle with you

Answer 14

is it 90 degrees or o

Answer 15

cos(90) = ???

Answer 16

1?

Answer 17

i mean 0

Answer 18

cos(90) = 0

Answer 19

so cos(pi/2) = 0

Answer 20

is the point (pi/2, 0) on the graph ?

Answer 21

no its not

Answer 22

so cos(x) is also out

Answer 23

tan(x) = ??? when x = 0

Answer 24

I always have trouble with tan im not really sure

Answer 25

tan =sin/cos

Answer 26

is it also 1?

Answer 27

tan(0) = sin(0)/cos(0)

Answer 28

so its 0?

Answer 29

yep

Answer 30

so tan is out because (0,0) is not on the graph

Answer 31

so far, we've tested and eliminated sin, cos, and tan

Answer 32

you need to test all 6, which are

sin, cos, tan
csc, sec, cot

Answer 33

so you have 3 left to test

Answer 34

how can i do those?

Answer 35

csc(0) = 1/sin(0) = ???

Answer 36

0?

Answer 37

sin(0) is what

Answer 38

0

Answer 39

so

csc(0) = 1/sin(0)

means

csc(0) = 1/0

but can you divide by zero?

Answer 40

no so its undefined?

Answer 41

so csc is out because the unknown function in the given graph is defined at x = 0

Answer 42

sec(0) = 1/cos(0) = ???

Answer 43

its also undefined

Answer 44

cos(0) = ???

Answer 45

1

Answer 46

sec(0) = 1/cos(0) = 1/1 = 1

so sec(0) = 1

Answer 47

sec(pi/2) = 1/cos(pi/2) = ???

Answer 48

1

Answer 49

cos(pi/2) = ???

Answer 50

0

Answer 51

sec(pi/2) = 1/cos(pi/2) = 1/0 = ???

Answer 52

undefined

Answer 53

good

Answer 54

so there's a vertical asymptote at x = pi/2, just like the graph shows

Answer 55

so sec(x) is a good candidate

Answer 56

we can test cot(x) to get

cot(0) = 1/tan(0) = 1/0 = undefined

so cot(x) is out

Answer 57

so we've eliminated everything but sec(x)

Answer 58

so its secant because of the vertical asymptote?

Answer 59

and because sec(0) = 1

Answer 60

csc has vertical asymptotes, but csc(0) = undefined

Answer 61

oh okay so those are the two reasons why?

Answer 62

yes the two basic reasons, you can test other values of x and you'll see they produce points on that graph

Answer 63

oh okay thank you so much!

Answer 64

np