P2.6 Trig. Functions

Question 1

what are sec, cosec & cot?

Answer 1

sec = 1/cos
cosec = 1/sin
cot = 1/tan

Question 2

how do you write cot?

Answer 2

cos/sin

Question 3

describe the graph of y=secx

Answer 3

symmetry in y-axis
period 360 degrees/2π
vertical asymptotes where cosx = 0 (90,270,450)
domain: x = real but not 90,270,450…
range is y ≤ -1 or y≥ 1

Question 4

describe the graph of y=cosecx

Answer 4

period 360 degrees/2π
vertical asymptotes where sinx = 0 (0,180,360)
domain: x = real but not 0,180,360…
range is y ≤ -1 or y≥ 1

Question 5

describe the graph of y=cotx

Answer 5

period 180 degrees/π
vertical asymptotes where tanx = 0 (180,360)
domain: x = real but not 0,180,360…
range is y = real

Question 6

CAST diagram

Question 7

1 + tan^2x =

Answer 7

sec^2x

Question 8

1 + cot^2x =

Answer 8

cosec^2x

Question 9

describe the graph of y=arcsinx

Answer 9

domain is -1 ≤ x ≤ 1
range is -π/2 ≤ arcsinx ≤ π/2
= -90 ≤ arcsinx ≤ 90

Question 10

describe the graph of y=arccosx

Answer 10

domain is -1 ≤ x ≤ 1
range is 0 ≤ arccosx ≤ π
= 0 ≤ arccosx ≤ 180

Question 11

describe the graph of y=arctanx

Answer 11

domain is x=real
range is -π/2 ≤ arctanx ≤ π/2
= -90 ≤ arctanx ≤ 90

Question 12

why do inverse trig. graphs have a restrictied domain?

Answer 12

to ensure they are one-to-one functions