MATH 1330 Review for Final

MATH 1330 Review for Final
When: 5/11 Monday, 10am
Where: GAR 205(Garrison Gym)
Time: Approx. 100 min (depending on the number of questions)
Number of questions: Approx. 25
Some Multiple Choice , Some Free Response Questions
What is covered: Chapters 4, 5, 6,7.
For the free response part, please show your work neatly. Do not skip steps.
Calculators are not allowed.
What to BRING: Picture ID, Pencil, eraser. (You will write on the test.)
Handy Formulas
sin (s + t) = sin s cos t + cos s sin t
sin (s  t) = sin s cos t  cos s sin t
cos (s + t) = cos s cos t  sin s sin t
cos (s  t) = cos s cos t + sin s sin t
tan (s + t) =
tan ( s  t) =
tan s  tan t
1  tan s tan t
tan s  tan t
1  tan s tan t
cos(2t) = cos 2 t  sin 2 t
sin(2t) = 2sin t cos t
sin
1  cos s
s

2
2
cos
1  cos s
s

2
2
tan
sin s
s

2 1  cos s
1
Fill in the unit circle!
2
1) Suppose that  is an acute angle of a right triangle and that cos( ) 
Find sin( ) and tan( ) .
2 2
.
5
6) Evaluate
 5 
a) tan 
 3 
 5 
b) cot 
 6 
 2 
c) cos

 3 
 5 
d) sin  

 3 
 4 
e) csc

 3 
 7 
f) sec

 6 
 11 
g) sin 

 6 
 3 
h) cot 
 4 
 5 
i) tan  
 4 
 7 
j) cos 

 4 
3
7) Evaluate


a) tan 135 0

c) tan  45 0



e) tan  315 0

g) cos  60 0

i) sin 240 0


d) cot  225 0



k) cos 150 0

b) cos 360 0




f) sin  45 0
h) cos 300 0

j) sin 210 0



8) Find the exact value of the following expression:
 1
a) sin 1   
 2
 1 
b) cos 1  
3
 2 
 2

c) arcsin

 2 

2

d) arccos 

 2 
 
e) arctan 3
f) arctan 1
4
9) Find the exact value of the following expression:

 2 
a) sec sin 1   
 5 


 5 
b) cos tan 1   
 4 

10) Find the period, amplitude and the phase shift (horizontal shift).
1  
a) f (t )  12 cos t  
4
5


b) f (t )  12 sin  6t  
5

 

c) f ( x)  10 tan 5 x  
20 

5
11) Write a sine function with amplitude 10, horizontal shift 5 to the left, vertical shift 2 down, and
period 5.
12) In the right triangle ABC with right angle C, AB  10 and AC  9 . Find the six trigonometric
functions of angle A.
13) Find an equation for the sine function passing through (0,0) given that the first maximum point
 
on the right of the origin is  ,5  .
4 
6
14) f ( x)  5 sin(6 x)
What is the domain of this function?
What is the range of this function?
Graph the function over one period.
Label the intercepts, minimum/ maximum value(s) with an ordered pair.
7
Exercise: f ( x)  6 cos(2 x)
What is the domain of this function?
What is the range of this function?
Graph the function over one period.
Label the intercepts, minimum/ maximum value(s) with an ordered pair.
8
cos( x)
cot( x)
1) Simplify:

2) Simplify:
cos 2 ( x) 
3) Simplify:
tan( x) 
4) Given sin( x) 
tan( x)  cot( x)
tan( x)  cot( x)
cos( x)
1  sin( x)
1
2
, 90 0  x  180 0 , and sin( y )   , 180 0  y  270 0 ,
4
5
Find:
a) sin( x  y )
b) sin( x  y )
c) cos( x  y )
d) cos( x  y )
9
5) Given tan( x)  
1
, 90 0  x  180 0 ,
5
a) sin(2 x)
b) cos(2 x)
6) Given sin( x) 
3
 x
, where x is an acute angle, find sin  .
5
2
7) Find the following using the sum or difference formulas:
a) cos(75 0 )
b) sin(105 0 )
10
8) Solve the following equation over the interval [0,2 ) : 2 sin 2 ( x)  9 sin( x)  7  0
9) Find all solutions of the equation cos(4 x) 
1
over the interval [0,2 ) .
2
10) Find the area of triangle ABC if ∠B = 30° , c = 10 and a = 12.
11
11) ABC is a triangle with AB = 10, BC = 13, and AC = 7. Find cos(A).
12) The angle of elevation from a point that is 120 ft away from a building to the top of the building
is 250. Find the height of the building.
13) Two boats leave the dock at the same time and they travel with an angle of 1200 between them.
What is the distance between them after they each travel 4 miles?
12
14) Given a triangle ABC, A = 450, B = 300, BC = 60 cm, find AC.
15- a) Given a triangle ABC with AB = 6 cm and BC = 4, angle A measures 1200.
How many choices are there for the measure of angle C?
b) Given a triangle ABC with AB = 6 cm and BC = 4, angle A measures 300.
How many choices are there for the measure of angle C?
c) In triangle ABC with AB = 6, BC = 7, the measure of angle A is 30o. How many choices are
there for the measure of angle C?
13