Download Assignment #5: Trigonometry and the Unit Circle

Assignment #5: Trigonometry and the Unit Circle
Name: _____
Section 4.1
Show all work on the sheet provided and clearly indicate your answer. Use pencil
1. Sketch each angle in standard position. Change each degree measure to radian measure.
Express answer as an exact value (in terms of fractions of  )
1290
b) 329o
a)

5
radians
3
2
5
b)
radians
4. Which graph represents an angle in standard position with a measure of
A.
y
y
C.
x
B.
y
5
 rad?
8
x
y
D.
x
x
5. Determine one positive and one negative angle conterminal with each angle given. Careful
a)
318
b)
 500
c)
3
4
d)
7
4
6. Determine the arc length of a circle with radius 3.5 cm if it is subtended by a central angle of
4
3
radians. Round your answer to one decimal place. Show all work.
7. Determine the arc length of a circle with radius 6.8 cm if it is subtended by a central angle
of 1300. Round your answer to one decimal place.
8. Determine the measure of the central angle subtended by an arc length of 25.4 cm and a radius of
8.0 cm. Express the answer in radians to the tenths place and in degrees to the tenths place.
9. John cuts a slice from a circular ice cream cake with a diameter of 30 cm. His slice is in the shape of
a sector with an arc length of 8 cm. What is the measure of the central angle of the slice, in radians?
Round your answer to two decimal places, if necessary.
11. A Ferris wheel makes one revolution every 50 seconds. The diameter of the Ferris wheel is
25 metres. What angle does the Ferris wheel rotate though in 5 minutes. Express your
answer in radians in exact form and in degrees to one decimal place.
12. A bicycle wheel with a radius of 330 mm makes 40 revolutions per minute. How far does
the bicycle travel in 7.00 minute? Convert distance to metres and round to the nearest
tenths place.