Download Precalculus Review Section 4

Hon Math III: Unit 7 Test Circles Review
Find the equation of a circle in standard form and identify the center and radius of the
circle based on the given information.
1. The circle that is tangent to the
y-axis and center is (-5, 4).
2. The circle that is tangent to the
x-axis and center is (3,-2).
3. Center is (-3, 1) and goes through
(2, 4).
4. The endpoints of a diameter are at
(-2, -7) and (6, -1).
5. x2
+ y2 – 6x + 10y – 8 = 0
6. x2
+ y2 + 8y + 12 = 0
7. x2
+ y2 + 2y – 2 = 3x + y
8. x2
+ 5x + y2 = 4y + 4
Geometry of Circles Review
Hon Math III: Unit 7 Test Trigonometry Review
1 – 2: Find a positive and negative coterminal angle for the given angle.
(Full Rotation:  360  or  2 )
5
1.
2. - 462o
12
3 – 4: Identify the quadrant and Convert from degrees to exact radians (answers with π).
3. -210o
4. 390o
5 – 6: Identify the quadrant and Convert from radians to degrees.
7
3
5.
6. 
8
6
TRIG RATIOS (Triangle or Unit Circle):
Opp
or y
CAH : cos  
Hyp
Hyp
1
1
csc 

sec 
or
Opp sin 
y
SOH : sin  
Adj
or x
Hyp
TOA: tan  
Hyp
1
1

or
Adj cos 
x
cot  
Opp
y
or
Adj
x
Adj
1
x

or
Opp tan 
y
7 – 14: Find the exact value of the following (without a calculator – UNIT CIRCLE ).
 Be able to Label a blank Unit Circle with ALL ANGLES (Radian + Degree) and
COORDINATES
3
11
o
o
7. sin( 210 )
8. tan
9. sec 300
10. cos 
6
4
o
11. csc(450 )
12. cot
17
6
13. sin
3
2
15 – 17: Find the value of the other 5 trig. functions.
4
8
15. cos  ;  lies in IV. 16. sin  
and tan  0
5
17
o
14. cos 240
17. tan  
12
and sec  0
5
18 – 20: Complete the following triangles for the all missing sides and angles (Round to
two decimals)
e
D
F
Z
A
7
16
40º
d
y
c
6
32 º
E
X
B
a
C
9
Y
21 – 24: Word Problems
21. From a 90-foot lighthouse on the coast, a Coast Guard officer sights a boat in difficulty. The angle of
depression of the boat is 4.5  . How far is the boat from the shoreline?
22. Jeremiah is looking at the top of steeple that is 120 feet from where he is standing. The angle of
elevation from his eye is 67º, how tall is the steeple)?
23. A ship is just offshore of New York City. A sighting is taken of the Statue of Liberty, which is about
305 feet tall. If the angle of elevation to the top of the statue is 200, how far is the ship from the base
of the statue?
24. A 60-meter line is used to hold a hot air balloon from floating away. From the basket of the hot air
balloon, the breeze from the wind creates an angle of depression of 35o. What is the ground distance
of the hot air balloon to where it is held to the ground and what is the vertical distance the hot air
balloon is in the air?
25 – 29: Graphing Trigonometric Functions – Be able to provide the 5 essential points in your sketch
25. f ( x )  2 sin x  3
26. y  5 cos(4 x )

27. g( x )  cos( x )  2
3
28. y  3 sin( 6 x )  4
29. y  2 cos(5 x )  7