4.7--Inverse Trig Functions
Inverse trig functions have restricted domains.
- /2 ≤ sin-1x ≤ /2
- /2 ≤ tan-1x ≤ /2
0 ≤ cos-1x ≤ Find the exact value of each expression without a calculator:
1)
tan (sin-1(1/2))
2)
cos-1 (sin (-π/4))
3)
tan-1 (cos (-π))
4.7--Inverse Trig Functions
Use a calculator to evaluate each expression in both
degrees and radians:
4)
sin-1 (0.345)
5)
tan-1 (-2.509)
6)
sec-1 (4.116)
Find the exact value without using a calculator:
7)
sin-1(cos (5π/6))
8)
cos (tan-1(-1))
4.7--Inverse Trig Functions
9)
Form a right triangle to find an algebraic expression
equivalent to the given expression:
cos (arcsin (4x))
10)
Form a right triangle to find an algebraic expression
equivalent to the given expression:
tan (cos-1(3x/2))
(Example #6, p. 420)
4.7--Inverse Trig Functions
The bottom of a 20-foot replay screen at
Dodger Stadium is 45 feet above the playing
field. As you move away from the wall, the
angle formed by the screen at your eye changes.
There is a distance from the wall where the
angle is the greatest. What is that distance?
Evaluate:
11)
sin (tan-1(4/9))
12)
cos (sin-1(-6/7))
4.7--Inverse Trig Functions
Evaluate:
13)
sec (cot-1(-11/3))
14)
tan (csc-1(-9/2))
Evaluate without using a calculator. Give exact answers:
15)
cos (2 sin-1(1/3))
16)
csc (2 cos-1(-4/7))