Download 4-6 Inverse Trigonometric Functions

When t =
, sin t =
. Therefore, sin
–1 = .
ANSWER: 4-6 Inverse Trigonometric Functions
Find the exact value of each expression, if it
exists.
6. arccos 0
SOLUTION: 2. arcsin
Find a point on the unit circle on the interval
with an x-coordinate of 0.
SOLUTION: Find a point on the unit circle on the interval
with a y-coordinate of
.
When t =
, cos t = 0. Therefore, arccos 0 =
.
ANSWER: When t =
, sin t =
= . Therefore, arcsin
.
8. arccos (–1)
SOLUTION: ANSWER: Find a point on the unit circle on the interval
with an x-coordinate of –1.
4. sin – 1
SOLUTION: Find a point on the unit circle on the interval
with a y-coordinate of
.
When t =
, cos t = –1. Therefore, arccos (–1)=
.
ANSWER: 10. cos– 1
When t =
, sin t =
. Therefore, sin
–1 = .
SOLUTION: Find a point on the unit circle on the interval
ANSWER: with an x-coordinate of
.
6. arccos 0
SOLUTION: eSolutions Manual - Powered by Cognero
Find a point on the unit circle on the interval
with an x-coordinate of 0.
Page 1
When t =
, cos t = –1. Therefore, arccos (–1)=
.
ANSWER: ANSWER: 4-6 Inverse Trigonometric Functions
14. tan – 1 0
10. cos– 1
SOLUTION: SOLUTION: Find a point on the unit circle on the interval
Find a point on the unit circle on the interval
with an x-coordinate of
When t =
= 0.
–1
, cos t =
such that .
. Therefore, cos
=
ANSWER: .
When t = 0, tan t =
. Therefore, tan
–1
0 = 0.
ANSWER: 0
12. arctan (–
27. DRAG RACE A television camera is filming a )
SOLUTION: Find a point on the unit circle on the interval
such that =–
drag race. The camera rotates as the vehicles move
past it. The camera is 30 meters away from the
track. Consider θ and x as shown in the figure.
.
a. Write θ as a function of x.
b. Find θ when x = 6 meters and x = 14 meters.
SOLUTION: a. The relationship between θ and the sides is
When t =
arctan (–
, tan t =
)=
. Therefore,
.
ANSWER: 14. tan – 1 0
eSolutions Manual - Powered by Cognero
SOLUTION: Find a point on the unit circle on the interval
opposite and adjacent, so tan θ =
the inverse, θ = arctan
. After taking
.
b.
Page 2
When t = 0, tan t =
. Therefore, tan
–1
ANSWER: 0 = 0.
a. θ = arctan
4-6 ANSWER: Inverse Trigonometric Functions
b. 11.3 , 25.0
0
Find the exact value of each expression, if it
exists.
27. DRAG RACE A television camera is filming a drag race. The camera rotates as the vehicles move
past it. The camera is 30 meters away from the
track. Consider θ and x as shown in the figure.
30. SOLUTION: The inverse property applies, because
lies on the interval [–1, 1]. Therefore,
=
ANSWER: a. Write θ as a function of x.
b. Find θ when x = 6 meters and x = 14 meters.
SOLUTION: a. The relationship between θ and the sides is
opposite and adjacent, so tan θ =
.
32. cos– 1 (cos π)
SOLUTION: . After taking
The inverse property applies, because π lies on the
the inverse, θ = arctan
interval
.
–1
. Therefore, cos
(cos π)= π.
ANSWER: b.
34. SOLUTION: The inverse property applies, because
interval
. Therefore,
lies on the =
.
ANSWER: ANSWER: a. θ = arctan
b. 11.3 , 25.0
Find the exact value of each expression, if it
exists.
30. eSolutions Manual - Powered by Cognero
SOLUTION: Page 3