Physics, Foundation Programme – Problem Solving Exercises 6
Trigonometric Functions
1. *Find the measure of (if possible) of the complement and the supplement of each angle:
a) a: cpl= spl=
b) a: cpl= spl=
c) a: cpl= spl=
d) a: cpl= spl:
2. Determine measure of the positive angle with measure less than 360º that is coterminal angle with given
angle and the classify the angle by quadrant. Assume the angles are in the standard position.
a) a: Q=III
b) a: Q=I
c) a: Q=II
3. Use a calculator to convert each DMS measure to its equivalent decimal degree measure.
a) a:
b) a:
4. Convert each decimal degree measure to its equivalent DMS measure
a) a:
b) a:
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5. Convert the degree measure to the exact radian measure
a) a:
b) a:
6. Find the length of an arc that subtends a central angle with the given measure in a circle with the given
radius. Round the answers to the nearest hundredth.
a) a: 6.28 cm
b) a: 12.57 m
7. * Each tire of a bicycle has a radius of 0.31 meters. The tires are rotating 4 revolutions per second. Find the
speed of the bicycle to the nearest tenth of meters per second.
A: 7.8 m/s
8. Find the values of the functions sin, cos, and tan of θ for the right triangle:
a)
a:
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b)
a:
9. The angle of elevation from a point 116 meters from the base of the Eiffel Tower to the top of the tower is
68.9º. Find the approximate height of the tower in meters.
a: 301 m
10. The angle of depression to one side of a lake, measured from a balloon 2500 feet above the lake as shown
in the accompanying figure, is 43º. The angle of depression to the opposite side of the lake is 27 . Find the
width of the lake.
a: 7587 ft ≈ 2313 m
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11. Find the value of each of the trigonometric functions sin, cos, and tan for the angle, in standard
position, whose terminal side passes through the given point.
a) P(2,3) a:
b) P(-2,3) a:
c) P(-6,-9) a:
12. Evaluate the trigonometric functions of the indicated angles, or state that the function is undefined.
θ 0º 90º 180º
sin(θ) 0 1 -1 0
cos(θ) 1 0 0 -1
tan(θ) 0 undef. undef. 0
13. State the amplitude, and period of the function defined by each equation
a) a:
b) a:
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c) a:
d) a:
14. *One cycle of the graph of a sine or cosine function is show. Find an equation of each of graph.
a)
a:
b)
a:
c)
a:
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15. Find the amplitude, phase shift and period for the graph of each function.
a) a:
b) a:
c) a:
16. * Each graph displays one cycle of the graph of a trigonometric function. Find an equation of each graph.
a)
a:
b)
a:
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c)
a:
17. The function
,
gives the blood pressure in millimeters of mercury (mm Hg), of a patient during a 20-second interval. Here,
t is time in seconds.
a. Find the phase shift and the period of
a:
b. What are the patient’s maximum (systolic ) and minimum (diastolic ) blood pressure readings during the
given time interval?
a: M=144 mmHg, m=80 mmHg
c. What is the patient’s pulse rate in beats per minute?
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18. Find exact radian value:
a) a:
b) a:
c) a:
d) a:
19. Use a calculator to approximate each function accurate to four decimal places
a) a: 57.37º, 1.001 radian
b) a: 92.04º, 1.606 radian
c) a: 75.09º, 1.3106 radian
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