Math 113 Carter Test 1
1. For each of the following equations:
(a) (2 points each equation) Classify as a parabola, an ellipse, or hyperbola, or a
degeneration of one of these;
(b) (4 points each equation) Complete the squares
(c) (3 points each equation) Determine the coordinates of the “center;”
(d) (3 points each equation) Determine the location of the focus or foci;
(e) (3 points each equation) Sketch the graph;
(f) (3 points each equation) Determine the intersections with the coordinate axes if
there are any;
i.
x2
−6x−3y2+18y=64
ii.
x2
−8x−3y2=65
iii.
y=20x2
2. ( 9 points) On the day of the vernal equinox, a 120 foot tall building at the equator
casts a 207.85 foot shadow to the west. If sunrise is 6:00AM, what time is it when the
shadow is cast?
3. ( 9 points) Use your calculator to determine the angle θin degrees when csc(θ)=1.557.
4. ( 9 points) Determine the remaining sides of a right triangle if γ=90
◦,a= 12, and
b=5.
5. ( 9 points) Find the exact values of the six trigonometric functions for an angle of π/3.
6. ( 9 points) Looking up from the water fountain in the park, a person observes that
the top of a building is at an angle of 37◦. The person has a 1 meter stride and paces
the straightline distance to the building to be 160 meters. How tall is the building in
meters?
1
