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Final Exam Topic Guide
MATH 1112A
Graphs of trigonometric functions (including amplitude, frequency/period, phase shifts)
and inverse trigonometric function; Graphs of conic sections;
Recognizing equations with or without transformations: vertical shift, horizontal shifts,
reflections across the x-axis, y-axis, and y=x line.
Solving trigonometric equations.
Finding exact values and coordinates using trigonometric identities.
Simplifying trigonometric expressions using identities.
DeMoivre’s Theorem
Conic Sections-recognizing type of graph with equation and total number of points of
intersections
Final Exam Sample Questions
1. If sin  > 0 and sec < 0, in which quadrant does the terminal side of the angle
lie?
a) I
b) II
c) III
d) IV
2. Expressed as a function of a positive acute angle, sin (-230°) is equal to:
a) sin (50°)
b) -sin (50°)
3. In the accompanying diagram of a
3 1
, )
unit circle, the ordered pair (
2
2
represents the point where the terminal
side of θ intersects the unit circle.
What is the m ?
a) 210°
c) 233°
b) 225°
d) 240°
c) cos (50°)
d) -cos (50°)
4. The path traveled by a roller coaster is modeled by the equation:
y  27 sin(13x)  30 . What is the maximum altitude of the roller coaster? (hint: how
is altitude is not the same as amplitude, but it is related.
a) 13
b) 27
c) 30
d) 57
5. A dog has a 20-foot leash attached to the
corner where a garage and a fence meet, as
shown in the accompanying diagram. When
the dog pulls the leas tight and walks from
the fence to the garage, the arc the leash
makes is 55.8 feet.
What is the m between the garage and
the fence, in radians?
a) 0.36
b) 2.79
c) 3.14
d) 160
6. If θ is an angle in standard position and P(-3,4) is a point on the terminal side of
θ, what is the value of sin θ?
a)
3
5
b) 
3
5
c)
4
5
d) 
4
5
7. In physics class, Eva noticed
the pattern shown in the
accompanying diagram on an
oscilloscope. Which equation best
represents the pattern shown on
the oscilloscope?
b)
1
y  sin( x)  1
2
y  2sin x  1
c)
y  sin x  1
d)
1
y  2sin(  x)  1
2
a)
8. What is the radian measure of the angle formed by the hands of a clock at
2:00pm
a)


b)
2
3

c)
d)
4

6
9. If A and B are positive acute angles, sin A 
of sin( A  B ) ?
16
a) 
65
10. If sin x 
cos( x  y ) ?
a) 
b)
33
65
c)
5
4
, and cos B  , what is the value
13
5
56
65
d)
63
65
12
3
, cos y  , and x and y are acute angles, what is the value of
13
5
33
65
b) 
14
65
c)
21
65
d)
63
65
5
, what is the value of sin 2 ?
13
60
120
c)
d)
169
169
11. If  is an acute angle such that sin  
a)
10
26
b)
12
13
12. The expression (1  cos x)(1  cos x) is equivalent to
a) 1
13. The expression
a) sin
14. The expression
a) sin
15. The expression
a)
cos 2 
sin 
b) sin 2 x
c) sec2 x
d ) csc2 x
2 cos 
is equivalent to
sin 2
b) sec
c) csc
d ) cot
sec 
is equivalent to
csc 
b) cos
c) tan
d ) cot
tan 
is equivalent to
sec 
sin 
b)
cos 2 
c) sin
d ) cos
16. The expression cos 40 cos10  sin 40 sin10 is equivalent to
a) cos30
b) cos50
c) sin30
d ) sin50
17. What value of x in the interval 0  x <180 satisfies the equation
2 cos 2 x  cos x  1?
a)  30
b) 30
c ) 60
d ) 150
18. The center of a circle represented by the equation ( x  2)2  ( y  3)2  100 is
located in Quadrant:
a) I
b) II
c) III
d ) IV
19. What is the equation of a circle with center (-3,1) and radius 7?
a) ( x  3)2  ( y  1)2  7
b) ( x  3) 2  ( y  1) 2  49
c) ( x  3)2  ( y  1) 2  7
d ) ( x  3) 2  ( y  1) 2  49
20. A circle has the equation ( x  1)2  ( y  3)2  16 . What are the coordinates of its
center and the length of its radius?
a) (-1,3) and 4
b) (1,-3) and 4
c) (-1,3) and 16
d ) (1,-3) and 16
21. A commercial artist plans to include an ellipse in a design and wants the length
of the horizontal axis to equal 10 and the length of the vertical axis to equal 6.
Which equation could represent the ellipse?
a) 9x 2 +25y2 =225
b) 9x 2 -25y 2 =225
c) x 2 +y2 =100
d ) 3y=20x 2
22. The accompanying diagram shows the
construction of a model of an elliptical orbit of
a planet travelling around a star. Point P and
the center of the star represent the foci of the
orbit.
Which equation could represent the relation
shown?
a)
x2 y 2
+
=1
81 225
b)
x2 y 2
+ =1
225 81
c)
x2 y 2
+ =1
15 9
d)
x2 y 2

1
15 9
23. Which equation, when graphed on a Cartesian coordinate plane, would best
represent an elliptical racetrack?
a) 3x 2 +10y2 =288,000
b) 3x 2 -10y2 =288,000
c) 3x+10y=288,000
24. An object orbiting a planet travels in a path represented by the equation
3( y  1)2  5( x  4)2  15 . In which type of pattern does the object travel?
a) parabola
b) circle
c) ellipse
d ) hyperbola
25. Which equation represents a hyperbola?
a) y2 =16-x 2
b) y=16-x 2
c) y=16x 2
Resource: New York Math B Regents
d ) y2  16  x 2
d ) 30xy=288,000