Download Midterm I Solutions - Bakersfield College

Math B1B Midterm I Solutions
Use the following triangle to answer # 1 - 6:
1a.
cos  =
1b.
cos  =
2a.
2b.
3a.
sec  =
3b.
csc(– =
4a.
sin
4b.
cos–
5a.
5b.
6a.
7. Suppose that
6b.
and
. Then
tan  = ?
7.
8. Suppose that
and
. Then
8.
cot =
9. What is the period of the function
?
9.
10. Find the area of the given triangle (the angle is in radians).
Round off your answer to the nearest hundredth.
This triangle isn't really a valid one;
there are two approaches, that yield
different answers. Either answer was
marked as correct.
Solution 1: Using the fact that a right triangle has area equal to half of that of its corresponding
rectangle,
Solution 2: Using the area formula, we get
, or about
10.
11. If
and
is in Quadrant I, express
as a function of
, and
Since
, we can construct the following triangle:
Then,
12. Use an angle sum identity to simplify this expression to a single term.
sin(A + B) cos(A – B ) – cos(A + B) sin(A – B) = ?
Let
, and
. Then the expression above becomes:
=
13. Continuing from problem 12, suppose that
=
and
Then what number does your expression from problem 12 equal ?
.
.
24.82
14. If
cm, then
Round off your answer to the nearest thousandth of a cm.
15. Write in terms of sine and cosine and simplify completely, making use of
the Pythagorean identities, as needed.
16. Simplify completely, making use of the Pythagorean identities, as needed. Write your answer in
terms of sines and cosines.
17. Suppose the given graph is a cosine with amplitude 5 and period 8. Find the coordinates of the
given point.
17. A = ( 12 , – 5 )
18. Find the solutions to the equation
--->
,
--->
in Quadrants I and IV.
or
(but this one's impossible)
--->
19. & 20. Find ALL real solutions to the equation in 18.
or
for any
in the integers
or
Extra Credit!
Find the exact area of a regular dodecagon inscribed inside a circle of radius 1. Also give the
difference between that exact area and , to the nearest millionth.
Area = A = 3
= 0.141593
We have
radians for a complete circle, so
.
Since the radius is 1, the area of one little wedge is
Since there are 12 wedges, the area of the dodecagon is thus:
So
rounded off to the nearest millionth: 0.141593
,