Download Inverse Trig Problems - AlexanderAcademics.com

Inverse Trig Differentiation from Larson/Hostetler
Evaluate each without using a calculator.
( )
1.
arcsin 12
2.
arcsin 0
3.
arccos 1 2
4.
arccos 0
5.
6.
cot (−1)
7.
sec
arctan 3 3
⎛
⎞
arccos⎜ − 3 2 ⎟
⎝
⎠
9.
arctan( − 3 )
−1
(− 2 )
8.
−1
10. Use your calculator to help make a careful sketch the graphs of each of the six
inverse trig functions. Include appropriate range restrictions.
Evaluate each without a calculator.
11.
14.
17.
(
(
)
sin arctan 3 4
cos arcsin 5 13
csc arctan − 5 12
(
(
)
))
12.
15.
18.
⎛
⎞
tan⎜ arccos 2 2 ⎟
⎝
⎠
cot arcsin − 1 2
tan arcsin − 5 6
(
(
13.
))
))
(
(
16.
(
)
sec arcsin 4 5
sec arctan − 3
(
( 5))
Solve each equation.
19.
21.
arcsin(3x − π ) = 12
arcsin 2x = arccos x
20.
arctan( 2x ) = −1
22.
cos −1 x = sec−1 x
Differentiate and simplify each.
23.
f (x ) = 2arcsin( x − 1)
24.
26.
f (x ) = arcsec(2x )
arcsin 3x
g( x ) =
x
29.
25.
g( x ) = 3arccos x 2
27.
f (t ) = arcsin t 2
f (x ) = arctan x
28.
f (x ) = arctan x
30.
h( x ) = x arctan x
31.
h(t ) = sin (arccost )
( a)
32.
f (x ) = arcsin( x ) + arccos( x )
33.
34.
2
y = xarcsin( x ) + 1− x
35.
(
1
2
x 1− x + arcsin( x )
2
y = arcsin x + x 1− x 2
y=
)