College Trigonometry, 2011a

10.6 The Inverse Trigonometric Functions 847
220. f(x) =− cos(x) − 2 √ 2sin(x) 221. f(x) =2sin(x) − cos(x)
In Exercises 222 - 233, find the domain of the given function. Write your answers in interval
notation.
222. f(x) = arcsin(5x)
( ) 3x − 1
223. f(x) = arccos
2
224. f(x) =arcsin ( 2x 2)
( )
( )
1
2x
225. f(x) = arccos
x 2 226. f(x) = arctan(4x) 227. f(x) = arccot
− 4
x 2 − 9
228. f(x) = arctan(ln(2x − 1)) 229. f(x) = arccot( √ 2x − 1) 230. f(x) = arcsec(12x)
( ) x
3
231. f(x) = arccsc(x +5) 232. f(x) = arcsec
233. f(x) = arccsc ( e 2x)
8
( 1
[
234. Show that arcsec(x) = arccos for |x| ≥1aslongasweuse 0,
x)
π ) ( π
]
∪
2 2 ,π as the range
of f(x) = arcsec(x).
( 1
235. Show that arccsc(x) =arcsin for |x| ≥1aslongasweuse
[−
x)
π ) (
2 , 0 ∪ 0, π ]
as the range
2
of f(x) = arccsc(x).
236. Show that arcsin(x) + arccos(x) = π for −1 ≤ x ≤ 1.
2
( 1
237. Discuss with your classmates why arcsin ≠30
2)
◦ .
238. Use the following picture and the series of exercises on the next page to show that
arctan(1) + arctan(2) + arctan(3) = π
y
D(2, 3)
A(0, 1)
α β γ
x
O(0, 0) B(1, 0) C(2, 0)