Math 104 – Review for Test #3
Identities Components
Equations Applications Addition
5
5
5
5
5
10
10
10
10
10
25
25
25
25
25
50
50
50
50
50
100
100
100
100
FINAL
Identities
5 Point Question
Is the following an equation or an identity?
cos( 2 x)  (cos x  sin x)
Equation
Go Home
Check
Work
2
10 Point Question
Verify the identity:
tan x
sec x 
sin x
Replace sec(x) with 1/cos(x), then
multiply by (sin(x)/sin(x)).
Go Home
Check
Work
25 Point Question
Verify the identity
cos( 2 x)
cos( x)  sin( x) 
cos( x)  sin( x)
Use cos(2x)=cos2(x)-sin2(x) and
factor.
Go Home
Check
Work
50 Point Question
Verify the identity:
2
sec x
2

csc
x

0
2
1  sec x
Convert to sines and cosines, use the
Pythagorean identity twice.
Go Home
Check
Work
Keep Score
100 Point Question
Verify the identity:
(cot(x) + cot(y)) sin(x) sin(y) = sin(x+y)
Convert cot(x) to cos(x)/sin(x), cot(y)
to cos(y)/sin(y), distribute, cancel and
you are done.
Go Home
Check
Work
Components
5 Point Question
A vector has magnitude of 6 and direction
angle of 325°. Write the vector in
component form.
4.91i – 3.44j
Go Home
Check
Work
Keep Score
10 Point Question
Find the magnitude and direction
angle for the vector 6i - 8j
Magnitude = 10
Direction angle = 306.9°
Go Home
Check
Work
Keep Score
25 Point Question
If u + v = 0, and u = -2i+5j, what is v?
v=2i-5j
Go Home
Check
Work
Keep Score
50 Point Question
Car A is traveling with velocity vector 21i +
35j. Car B is traveling wit velocity vector
40j. Which car is traveling faster?
Car A
Go Home
Check
Work
Keep Score
100 Point Question
Given ux= -5 and  = 120°, find uy
uy = 8.66
Go Home
Check
Work
Keep Score
Equations
5 Point Question
Solve: sin(x) = 1/2
0
X=30
or
0
0
150 + 360 k
Go Home
0
+360 k
Check
Work
10 Point Question
Solve the equation 5cos(x)-4=0
X=0.6435 + 2Pi k or
X=-0.6435 + 2Pi k
Go Home
Check
Work
Keep Score
25 Point Question
Solve the equation 3tan2x-1=0
X=300 + 1800k
0
0
Or x=-30 + 180 k
Go Home
Check
Work
50 Point Question
Solve: cos(2x)-cos(x)=-1
0
0
X=90 +180 k
or
0
0
0
+360 k or - 60 +360 k
Go Home
Check
Work
0
60
100 Point Question
Solve:
2sin2(3x)-sin(3x)-1=0

2
x

k,
6
3
7
2
x

k
18
3
11
2
x

k
18
3
Go Home
Check
Work
Keep Score
Applications
5 Point Question
A scout travels 300 yards in the direction
N40°W. Write this vector in component
form.
-192.8i+229.8j
Go Home
Check
Work
Keep Score
10 Point Question
What third force is required to keep 2i + 3j
and –4i +3j in check?
2i – 6j
Go Home
Check
Work
Keep Score
25 Point Question
A boat travels S 50° W for 14 miles, then
travels N 10° E for 5 miles. What course
and distance must the boat travel to make it
back to its starting point?
10.66 mi at N67.5°E
Go Home
Check
Work
Keep Score
50 Point Question
A plane is flying at 200 miles per hour in
the direction S 15° E. The wind is blowing
due north at 30 miles per hour. What is
the true speed and direction of the plane?
171.2 mph S17.6ºE
Go Home
Check
Work
Keep Score
100 Point Question
A 200 lb weight is suspended by two cables
in the drawing below. How big is the tension
in each cable?
25°
25°
236.6 lbs
Go Home
Check
Work
Keep Score
Addition
5 Point Question
U = 2i + 3j, V = -3i + 2j - 4k
Find U + V.
U + V = -i + 5j – 4k
Go Home
Check
Work
Keep Score
10 Point Question
Sketch the sum of the two vectors.
Go Home
Check
Work
Keep Score
25 Point Question
u has a magnitude of 8 and a direction
angle of 150º. v has a magnitude of 3 and a
direction angle of 280°. Find u + v.
-6.407i+1.046j
Go Home
Check
Work
Keep Score
50 Point Question
Find x and y if (y2 i + 4xj) + (– 9i + 8j) = 0
x = -2 and y = -3 or 3
Go Home
Check
Work
Keep Score
FINAL QUESTION
A 3000 lb car is parked on a 15° incline.
What force is required to keep it from
rolling down the incline?
776.457 lbs
Go Home
Check
Work
Keep Score