Inverse Trig Functions

Question 0

Range of arccos

Answer 0

0 to pie

Quadrants 1 and 2

Question 1

Range of arcsin

Answer 1

• pie. Pie
• —- to —-
  
  2. 2

Quadrants 4 and 1

Question 2

Range of arctan

Answer 2

• pie. Pie
• —- to —-
  
  2. 2

Quadrants 4 and 1

Question 3

Range of arccot

Answer 3

0 to pie

Quadrants 1 and 2

Question 4

Range of arcsec

Answer 4

0 to pie
y cannot equal pie/2

Quadrants 1 and 2

Question 5

Range of arccsc

Answer 5

-pie. Pie
—– to —-
2. 2
y cannot equal 0

Quadrants 4 and 1

Question 6

Derivative of arcsin u

Answer 6

u’
y’ = —————————
Square root of 1 - u^2

Question 7

Derivative of arccos u

Answer 7

• u’
  y’ = —————————
  Square root of 1 - u^2

Question 8

Derivative of arctan u

Answer 8

u’
y’ = ———-
1 + u^2

Question 9

Derivative of arccot u

Answer 9

-u’
y’ = ———-
1 + u^2

Question 10

Derivative of arcsec u

Answer 10

u’
y’ = ——————————–
|u| square root of ( u^2 - 1 )

Question 11

Derivative of arccsc u

Answer 11

-u’
y’ = ——————————–
|u| square root of ( u^2 - 1 )

Question 12

du
Integral of —————————
Square root ( a^2 - u^2 )

Answer 12

u
Arcsin — + C
a

Question 13

du
Integral of ————-
a^2 + u^2

Answer 13

1 u
— Arctan — + C
a a

Question 14

du
Integral of —————————
u square root ( u^2 - a^2 )

Answer 14

1 |u|
— Arcsec — + C
a a