P2.6 Trig. Functions

Question 1

what are secx, cosecx & cotx?

Answer 1

secx = 1/cosx
cosecx = 1/sinx
cotx = 1/tanx

undefined for values of x for which cosx, sinx & tanx = 0

Question 2

cotx =

Answer 2

cosx / sinx

Question 3

sketch & 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

sketch & 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

sketch & 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

when do secx = k & cosecx = k have no solutions?

Answer 7

-1 < k < 1

Question 8

1 + tan^2x =

Answer 8

sec^2x

Question 9

1 + cot^2x =

Answer 9

cosec^2x

Question 10

sketch & describe the graph of y=arcsinx

Answer 10

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

Question 11

sketch & describe the graph of y=arccosx

Answer 11

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

Question 12

sketch & describe the graph of y=arctanx

Answer 12

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

Question 13

why do inverse trig. graphs have a restrictied domain?

Answer 13

to ensure they are one-to-one functions