MATH 115 QUIZ 5 SOLUTIONS
December, 2016
Instructor: S. Sands
1. (6 pts) The note 'A' below the note 'middle C' is a sound wave with ordinary frequency
f
= 220 Hertz
= 220 cycles/second. State a sinusoid which models this note, assuming that the amplitude is 1 and the
phase shift is 0.
(no explanation required) [section 11.1, p. 881 and exercise 11.1, #1]
g1845g4666g1872g4667 = g1827 sing4666g2033g1872 + g2030g4667
2. (10 pts) Solve the equation
sing4666g1876g4667 tang4666g1876g4667 + uni221A3
sing4666g1876g4667 = 0
, finding all solutions in the
interval [0, 360
°
).
Show work
.
HINT: Note that sin(
x
) is a factor.
(You should be able to provide the exact
values of the solutions and state them in degrees.) [Section 10.7]
°
(chart on page 724 is a helpful reference; for tangent
look for ratio of
y
/
x
=
−uni221A3
)
°
3. (8 pts) Solve the equation
4 arccosg46665g1876g4667 = 3g2024
. Find the exact value(s). HINT: Write an appropriate
corresponding equation involving sine.
Show work.
.
[Section 10.7]
4. (10 pts) Solve the equation
sing46662g1876g4667 + uni221A2
cosg4666g1876g4667 = 0
, finding all solutions in the interval [0, 2
π
).
Show work.
HINT: Start by applying an appropriate trig identity.
(You should be able to provide the exact
values of the solutions and state them in radians.)
[Section 10.7]
π
π
5. (12 pts) For the triangle
ABC
, we are given that
B
= 80
°
,
a
= 52.0, and
b
= 78.0.
(Side
a
is the side opposite angle
A
, side
b
is the side opposite angle
B
, and side
c
is the side opposite angle
Solve the triangle; that is, find the two remaining angles and the remaining side.
Report angles to the nearest degree and the length rounded to the nearest tenth.
Show work.
C
.)
