Homework Assignment
Solutions
3.6.1. Compute the following and leave your answers in exact
form.
(a) sin−1 21
◦
Answer:
30
(b) sin−1
Section 3.6
3
5.5
θ
√
3
2
Answer: 33.06◦
Answer:
60◦
√ 2
(c) cos−1 2
3.6.6. Find θ below. Round to two decimal places.
Answer: 45◦
√
(d) tan−1 ( 3)
Answer: 60◦
5
−1
(e) tan (1)
Answer: 45◦
θ
3.6.2. Compute the following and leave your answers in exact
form.
√
2
2
Answer: 1
(c) sin(sin−1 (0.34))
Answer: 0.34
(d) sin−1 (sin(120◦ ))
Answer: 60◦
(e) cos−1 (cos(−63◦ ))
Answer: 63◦
3.6.3. Find θ below.
places.
Answer: 23.96◦
Round your answer to two decimal
θ
2
5
Answer: 68.20◦
3.6.4. Find θ below.
places.
Answer: 22.62◦
3.6.7. The basepaths on a baseball diamond are 90 ft. On
a particular pitch, a baserunner tries to steal second
base. The runner is 40 ft away from first base when
the catcher catches the pitch. At this moment what
angle is the line between the catcher and the baserunner making with the first base line? Assume that the
catcher is exactly on the intersection of the first and
third base lines and assume that the baserunner is exactly on the line between first and second base. Round
your answer to two decimal places. Hint: It is less than
45◦ .
(a) cos−1 (sin(60◦ ))
◦
Answer:
30
(b) tan sin−1
13
Round your answer to two decimal
6
3.6.8. The grade of a road is calculated from its vertical rise
per 100 ft. For example, if a road is sloped such that it
climbs 5 ft for every 100 ft of horizontal distance trav5
eled then its grade is calculated to be 100
= 0.05. If
a particular road has a grade of 0.09, what is its angle
of incline? Round your answer to two decimal places.
Answer: 5.15◦
3.6.9. Christina is launching a model rocket. For safety reasons she clears a circle of radius 50 m around the launch
point. When she launches the rocket she launches it
at a slight angle so that when the rocket passes the
edge of the circle it is 250 m in the air. At what angle
was the rocket launched? Make sure that your angle is
measured from the ground (that is, your angle should
be between 0◦ and 90◦ ). Round to two decimal places.
Answer: 78.69◦
θ
10
Answer: 53.13◦
3.6.5. Find θ below.
places.
Round your answer to two decimal
Last Updated: March 29, 2014
3.6.10. A rope helps anchor a flag pole. The rope is tied to
the top of the flagpole at one end and is anchored into
the ground at the other end. The flag pole is 100 ft tall
and the rope is 125 ft long. What angle does the rope
make with the flag pole? Round to two decimal places.
Answer: 36.87◦
Page 1 of 2
Solutions
3.6.11. Stevie’s kite has a string which is 100 m long and,
at a particular moment, it is 70 m off of the ground.
What angle does the kite string make with the ground?
Round to two decimal places.
Answer: 44.43◦
3.6.12. Two birds - Dave and Jonas - fly out of their nest in
a tree. Dave flies 4 mi south and Jonas flies 7 mi east.
Later, Dave wants to fly to Jonas.
Section 3.6
Answer: 29.74
◦
nest
7 mi
Jonas
E
4 mi
Homework Assignment
θ
Dave
S
(a) How far will Dave need to fly? Round your answer to two decimal places.
Answer: 8.06 mi
(b) Dave needs to fly roughly northeast to get to
Jonas. At what angle north of east does he need
to fly? Round your answer to two decimal places.
(This angle is shown as θ below.)
Last Updated: March 29, 2014
3.6.13. Find the (acute) angle that the function f (x) = 2x + 3
makes with the horizontal. Round to two decimal
places.
Answer: 63.43◦
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