trig table midterm 1

Question 1

sin(x):
domain and range
derivative
inverse

Answer 1

d:[-π/2, π/2]
r: [-1,1]
d/dx= cos(x)
arcsin(x)

Question 2

cos(x):
domain and range
derivative
inverse

Answer 2

d: [0,π]
r: [-1,1]
d/dx= -sin(x)
arccos(x)

Question 3

tan(x):
domain and range
derivative
inverse

Answer 3

d: (-π/2, π/2)
r: (-∞, ∞)
d/dx= sec²(x)
arctan(x)

Question 4

cot(x):
domain and range
derivative
inverse

Answer 4

d: (0, π)
r: (-∞, ∞)
d/dx= -csc²(x)
arccot(x)

Question 5

sec(x):
domain and range
derivative
inverse

Answer 5

d: [0,π/2) U (π/2, π]
r: (-∞, ∞)
d/dx= sec(x)tan(x)
arcsec(x)

Question 6

csc(x):
domain and range
derivative
inverse

Answer 6

d: [-π/2, 0) U (0, π/2]
r: (-∞, ∞)
d/dx= -csc(x)cot(x)
arccsc(x)

Question 7

derivative of arcsin(x)

Answer 7

1/√(1- x²)

Question 8

derivative of arccos(x)

Answer 8

-1/√(1- x²)

Question 9

derivative of arctan(x)

Answer 9

1/(x²+1)

Question 10

derivative of arccot(x)

Answer 10

-1/(x²+1)

Question 11

derivative of arcsec(x)

Answer 11

1/(|x|√(x²-1)

Question 12

derivative of arccsc(x)

Answer 12

-1/(|x|√(x²-1)