Math 5 Trigonometry
Chapter 5 Test
fall ’06 Name_________________________
Show your work for credit. Write all responses on separate paper.
1.
What is the length of the arc subtended by an angle in a circle of radius 14?
2.
Find the central angle on a circle of radius 4 that
subtends and arc of length 6. Give both
the radian measure and the degree measure of the angle.
3.
What is the radius of a circle where a sector with central
angle of 36˚ has area = 9?
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4.
Three circles with radii 3, 5 and 12 are externally
tangent to one another, as shown in the figure at right. a.
Show that b.
Approximate to the nearest hundredth of a degree
measures for c. Find the area of the shaded region between the three circles. |
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5. A tricycle with little wheels of diameter 10cm and a big wheel with diameter 40cm is rolling along so that the big wheel is rolling at 35 rotations per minute.
a. What is the angular speed of the little wheels?
b.
What is the linear speed of the tricycle?
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6. The elongation α for Mercury is the angle formed by the planet, Earth and Sun, as shown in the diagram at right. Assume the distance from Mercury to the sun is 0.387 AU (38.7% of the distance from Earth to Sun) and that α = 18˚. Find the possible distances from Earth to Mercury. |
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7.
Find the area of the shaded region in the figure at
right. 8.
Approximate to the nearest hundredth of a degree, the
interior angles of a triangle with
sides 4, 5 and 6. 9.
Suppose an interior angle of a triangle measures 1
radian and is nested between sides of lengths 11 and 14. What is the length of the side opposite
that angle? 10. Suppose
we have vectors and a. Draw and label these vectors together in the x-y plane, assuming each has its initial point at (0,0). b. Find the angle between these two vectors. c.
Find the length of d.
Find the lengths of |
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