5.R: Trigonometric Functions (Review)
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- Apr 27, 2023
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5.1: Review Exercises
For the exercises 1-2, convert the angle measures to degrees.
1) \dfrac{π}{4}
- Answer
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45°
2) −\dfrac{5π}{3}
For the exercises 3-6, convert the angle measures to radians.
3) -210°
- Answer
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−\dfrac{7π}{6}
4) 180°
5) Find the length of an arc in a circle of radius 7 meters subtended by the central angle of 85°.
- Answer
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10.385 meters
6) Find the area of the sector of a circle with diameter 32 feet and an angle of \dfrac{3π}{5} radians.
For the exercises 7-8, find the angle between 0° and 360° that is coterminal with the given angle.
7) 420°
- Answer
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60°
8) −80°
For the exercises 9-10, find the angle between 0 and 2π in radians that is coterminal with the given angle.
9) − \dfrac{20π}{11}
- Answer
-
\dfrac{2π}{11}
10) \dfrac{14π}{5}
For the exercises 11-, draw the angle provided in standard position on the Cartesian plane.
11) -210°
- Answer
-
12) 75°
13) \dfrac{5π}{4}
- Answer
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14) −\dfrac{π}{3}
15) Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour.
- Answer
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1036.73 miles per hour
16) A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour?
5.2: Review Exercises
1) Find the exact value of \sin \dfrac{π}{3}.
- Answer
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\dfrac{\sqrt{3}}{2}
2) Find the exact value of \cos \dfrac{π}{4}.
3) Find the exact value of \cos π .
- Answer
-
-1
4) State the reference angle for 300°.
5) State the reference angle for \dfrac{3π}{4}.
- Answer
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\dfrac{π}{4}
6) Compute cosine of 330°.
7) Compute sine of \dfrac{5π}{4}.
- Answer
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−\dfrac{\sqrt{2}}{2}
8) State the domain of the sine and cosine functions.
9) State the range of the sine and cosine functions.
- Answer
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[–1,1]
5.3: Review Exercises
For the exercises 1-4, find the exact value of the given expression.
1) \cos \dfrac{π}{6}
2) \tan \dfrac{π}{4}
- Answer
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1
3) \csc \dfrac{π}{3}
4) \sec \dfrac{π}{4}
- Answer
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\sqrt{2}
For the exercises 4-12, use reference angles to evaluate the given expression.
5) \sec \dfrac{11π}{3}
6) \sec 315°
- Answer
-
\sqrt{2}
7) If \sec (t)=−2.5, what is the \sec (−t)?
8) If \tan (t)=−0.6 , what is the \tan (−t)?
- Answer
-
0.6
9) If \tan (t)=\dfrac{1}{3}, find \tan (t−π).
10) If \cos (t)= \dfrac{\sqrt{2}}{2}, find \sin (t+2π).
- Answer
-
\dfrac{\sqrt{2}}{2} or −\dfrac{\sqrt{2}}{2}
11) Which trigonometric functions are even?
12) Which trigonometric functions are odd?
- Answer
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sine, cosecant, tangent, cotangent
5.4: Review Exercises
For the exercises 1-5, use side lengths to evaluate.
1) \cos \dfrac{π}{4}
2) \cot \dfrac{π}{3}
- Answer
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\dfrac{\sqrt{3}}{3}
3) \tan \dfrac{π}{6}
4) \cos (\dfrac{π}{2}) = \sin ( \_\_°)
- Answer
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0
5) \csc (18°)= \sec (\_\_°)
For the exercises 6-7, use the given information to find the lengths of the other two sides of the right triangle.
6) \cos B= \dfrac{3}{5}, a=6
- Answer
-
b=8,c=10
7) \tan A = \dfrac{5}{9},b=6
For the exercises 8-9, use Figure below to evaluate each trigonometric function.
8) \sin A
- Answer
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\dfrac{11\sqrt{157}}{157}
9) \tan B
For the exercises 10-11, solve for the unknown sides of the given triangle.
10)
- Answer
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a=4, b=4
11)
12) A 15-ft ladder leans against a building so that the angle between the ground and the ladder is 70°. How high does the ladder reach up the side of the building?
- Answer
-
14.0954 ft
13) The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.
Practice Test
1) Convert \dfrac{5π}{6} radians to degrees.
- Answer
-
150°
2) Convert −620° to radians.
3) Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of 30°.
- Answer
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6.283 centimeters
4) Find the area of the sector with radius of 8 feet and an angle of \dfrac{5π}{4} radians.
5) Find the angle between 0° and 360° that is coterminal with 375°.
- Answer
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15°
6) Find the angle between 0 and 2π in radians that is coterminal with −\dfrac{4π}{7}.
7) Draw the angle 315° in standard position on the Cartesian plane.
- Answer
-
8) Draw the angle −\dfrac{π}{6} in standard position on the Cartesian plane.
9) A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?
- Answer
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3.351 feet per second, \dfrac{2π}{75} radians per second
10) Find the exact value of \sin \dfrac{π}{6}.
11) Compute sine of 240°.
- Answer
-
−\dfrac{\sqrt{3}}{2}
12) State the domain of the sine and cosine functions.
13) State the range of the sine and cosine functions.
- Answer
-
[ –1,1 ]
14) Find the exact value of \cot \dfrac{π}{4}.
15) Find the exact value of \tan \dfrac{π}{3}.
- Answer
-
\sqrt{3}
16) Use reference angles to evaluate \csc \dfrac{7π}{4}.
17) Use reference angles to evaluate \tan 210°.
- Answer
-
\dfrac{\sqrt{3}}{3}
18) If \csc t=0.68, what is the \csc (−t)?
19) If \cos t= \dfrac{\sqrt{3}}{2}, find \cos (t−2π).
- Answer
-
\dfrac{\sqrt{3}}{2}
20) Which trigonometric functions are even?
21) Find the missing angle: \cos \left(\dfrac{\pi }{6} \right)= \sin (\;)
- Answer
-
\dfrac{π}{3}
22) Find the missing sides of the triangle ABC: \sin B= \dfrac{3}{4},c=12
23) Find the missing sides of the triangle.
- Answer
-
a=\dfrac{9}{2},b=\dfrac{9\sqrt{3}}{2}
24) The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.