Trigonometry

Question 1

what is sec(x) equal to?

Answer 1

1/cos(x)

Question 2

What is cosec(x) equal to?

Answer 2

1/sin(x)

Question 3

What is cot(x) equal to?

Answer 3

1/tan(x) or cos(x)/sin(x)

Question 4

What is tan(x) equal to?

Answer 4

sin(x)/cos(x)

Question 5

What is the domain, range, period, symmetry and any asymptotes on the graph y = sec(x)?

Answer 5

domain - x can be every real but cant be equal to multiples of 90 degrees or pi radians
range - y is less than or equal to -1 or y is greater than or equal to one
period - 360 degrees 2pi radians
symmetry - y-axis
asymptotes - where cos(x) = 0

Question 6

What is the domain, range, period, symmetry and any asymptotes on the graph y = cosec(x)?

Answer 6

domain - x can be every real but cant be equal to multiples of 180 degrees or pi radians
range - y is less than or equal to -1 or y is greater than or equal to one
period - 360 degrees 2pi radians
symmetry - none
asymptotes - where sin(x) = 0

Question 7

What is the domain, range, period, symmetry and any asymptotes on the graph y = cot(x)?

Answer 7

domain - x can be every real but cant be equal to multiples of 180 degrees or pi radians
range - every real
period - 180 degrees pi radians
symmetry - none
asymptotes - where tan(x) = 0

Question 8

what is sec^2(x) equal to?

Answer 8

1 + tan^2(x)

Question 9

what is cosec^2(x) equal to?

Answer 9

1 + cot^2(x)

Question 10

What is the inverse function of sin(x) called and what is its domain and range?

Answer 10

arcsine(x) or sin^-1(x)
domain = -1 <= x <= 1
range -90 <= y <= 90

Question 11

What is the inverse function of cos(x) called and what is its domain and range?

Answer 11

arccosine(x) or cos^-1
domain = -1 <= x <= 1
range 0 <= y <= 180

Question 12

What is the inverse function of cos(x) called and what is its domain and range?

Answer 12

arccosine(x) or cos^-1
domain = -1 <= x <= 1
range 0 <= y <= 180