Math 181 Trigonometry

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Angles and Trigonometric Functions

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c. 933° MATH 181 (Trigonometry) Chapter 1 HW (Angles and Trigonometric Functions) Due Date February 27, 2019 1. Find the degree measures of two positive and two negative angles that are coterminal with each given angle. a. 30 b.-90° Determine whether 8", -368° are coterminal. 3. Name the quadrant in which each angle lies. a. 85 b.-125° 4. Find the degree measure of the smallest positive angle that is coterminal with each angle. b. -1100° 5. Convert each angle to decimal degrees. When necessary round to four decimal places. a. -8°30'18" b. 28°5'9" 6. Convert each angle to degree-minutes-seconds. Round to the nearest whole number of seconds. a. -17.33° b. 17.8° 7. Perform each computation without a calculator. a. 90° -7°44'35" b. (43°13'8)/2 8. Find degree measure of the angle a in the figure a. 540° ny 1400 19 16" Х C. 150° TE TT 6 3 4 TI 3 TT a. 3 9. Convert each degree to radian measure. Give exact answers in terms of 1). a. 45° b. 30° d. 225 10. Convert each radian measure to degree measure. 370 a. b. C. d. -67 11) Find the radian measure for two positive and two negative angles that are coterminal with the given angle. 270 a. b. 12. For each given angle name the quadrant in which the terminal side lies. 270 b. 13. Find the measure in radians (in terms of tt) of the smallest positive angle that is coterminal with each given angle 13п a. b. (14. Find the length of the arc intercepted by the given central angle a in a circle of radius r. Round to the nearest tenth. a. r = 12 ft b. a = 1.3, r = 26.1m 15. Find the radius of the circle in which the given central angle a intercepts an arc of the given length s. Round to the nearest tenth. a = 180°, s = 10km b. a == S = 500 ft 16. Find the exact area of the sector of the circle with the radius 6 and central angle a = 30° 970 2 3 TI a = a. Chair Loft. Oct 8.34 30. The angle of elevation of a pedestrian crosswalk over a busy highway is 8.34° as shown 33424 in the drawing. If the distance between the ends of the crosswalk measured on the ground is 342 ft, then what height, h, of the crosswalk at the center? (Round approximate answers to the nearest tenth) 31. A 41-m guy wire is attached to the top of a 34.6-m antenna and to a point on the ground. How far is the point on the ground from the base of the antenna (to the nearest meter), and what angle dies the guy wire make with the ground (to the nearest tenth)? 32. A boat sailing north sights a lighthouse to the east at an angle of 32 from the north as shown in the drawing. After the boat travels one more kilometer, the angle of the lighthouse from the north is 36°. If the boat continues to sail north, then how close will the boat come to the lighthouse to the nearest tenth of kilometer? 33. A contractor wants to pick up a 10-ft diameter pipe with a chain of length 40ft. The chain encircles the pipe and is attached to a hook on a crane. What is the distance between the hook and the pipe to the nearest thousandth of a foot. 34. Find cos a, given that sin a = 5/13 and a is in quadrant II. 35. Find sin a, given that cos a = 3/5 and a is in quadrant IV. 36. Sketch the given angle in standard position and find its reference angle in degrees and radians. a. 51/3 b. 405° 37. Use reference angle to find the exact value of each expression: a. cos(51/3) b. cos (-171/6) C. cos(-240°) 38. Use reference angle to find all six-trigonometric function for each given angle 0. a. 31/4 b. 41/3 d. -135° 39. True of False (do not use calculator) a. sin(179°) = - sin(1°) b. sin(231/24) = - sin(1/24) 40. A weight is suspended on a vertical spring. The weight is set in motion and its position x on the vertical number line is given by the function x = 4 sin(t) + 3 cos(t) where t is time in seconds a. Find the initial position of the weight (its position at times t = 0) b. Find the exact position of the weight at time t = 51/4 seconds. 41. The formula d = 1/32 ve sin(20) gives the distance d in feet that projectile will travel when its launch angle is 0 and its initial velocity is vo feet per second. Approximately what initial velocity in miles per hour does it take to throw a javelin 367 ft assuming that is 43°? Round to the nearest tenth. 42. Evaluate the trigonometric functions for the angle a in standard form position whose terminal side passes through (3,4) C. cot a b. csc a a. sec a 43. Find the exact value of each function. b. csc(-1/6) C. cot(1/3) a. sec(60°) c. 300° a. 1 rev * 1 rev b. * cos" TT 4 17. Find each product. Be sure to indicate the units for the answer. Round approximate answers to the nearest tenth. 55 rev 670 ft 10 rad 60 min 1 min 1 min 20 rad 1 hr bor 18. Perform each conversion. a. 30 rev/min rad/min b. 180 rev/sec = rad/hr. 19. A windmill for generating electricity has a blade that is 30 feet long. Depending on the wind, it rotates at various velocities. In each case, find the angular velocity in rad/sec (to the nearest tenth) for the dip of the blade. Use 30 days/month. a. 500 rev/sec b. 50,000 rec/day b edib 20. A common speed for an electric motor is 3450 revolutions per minute. Saw blades of various diameters can be attached to such a motor. Determine the linear velocity in mi/hr for a point on the edge of a blade with each given diameter. a. 6 in se tivno b. 14 in. 21. Find the exact value of each function without using a calculator. 810E 8.5 na da 69 119o a a. cos(90°) d. seci abno92 b. cot(21) e. sin(30°) EEI-6 c. sin() f. secl - to todose mohou 22. Find the exact value of each expression without using a calculator. oe gobbnin.8 a. c. sin + cos sinj b. sin( + 3 d. sin(30°)cos(135°) + cos(30°)sin(135) 23. Find the exact value of each expression for the given value of 0. Do not use a calculator. SV a. sin(20) if 0 = 1/4 b. sin(0/2) if 0 = 31/2 24. If sin a = 0, then what is csc a? 25. Find the acute angle a (in degrees) that satisfies each equation. Do not use calculator. a. sin a = 1/2 b. tan a = V3 26. Evaluate each expression without using a calculator. Give the result in degrees. a. cos (1/2) b. tan^(0) 27. Find the exact values of all six trigonometric functions for the angle a in each given right triangle. b. 9 h $481 It 3 28. Solve each right triangle with the give sides and angles. In each case, make a sketch. Round approximate answers to the nearest tenth. a. a = 6, b = 8 b. a = 39'9', a = 9 29. An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads. The photograph is made when the angle of elevation of the sun is 32°. By comparing the shadow cast by the building to objects of known size in the photographs, analysts determine that the shadow is goft long. How tall is the building (to the nearest foot)? BUIL DING a. 232 -Soft
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Solution

1. Coterminal Angles are angles who share the same initial side and terminal sides. Finding
coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on
whether the given angle is in degrees or radians.
A) Positive coterminals of 30
i.
30 + 360 = 390
ii.
30+2(360) = 750
Negative coterminals
i.
ii.

30 – 360 = -330
30- 360(2) = -690

B) Positive coterminals of -90
i.
-90+360 = 270
ii.
-90+2(360) = 630
Negative coterminals
i.
ii.

-90 – 360 = -450
-90- 360(2) = -810

2. Difference between two coterminal angle is 360 or a multiple of 360 degrees. Therefore;
8 – (-368) = 376. Therefore the two are not coterminals

3. Quadrants:
I – (0-90)
II(90-180)
III(180-270)
IV(270-360)

Therefore: A) 85 deg - 1st quadrant
B)-125 positive equivalent is (360 – 125) = 235 hence 3rd quadrant

C) 933 is the coterminal of (933 - 360(2) = 213) hence 3rd quadrant

4. A. 540 – 360 = 180
B. -1100 + 4(360) = 340

5. A.
= -8° 30' 18"
= -8° - 30'/60 -18"/3600
= - 8.505°
B.
= 28° 5' 9"
= 28° + 5'/60 + 9"/3600
= 28.08583°

6. A.
d = int(17.33°) = 17°
m = int((17.33° - 17°) × 60) = 19'
s = (17.33° - 17° - 19'/60) × 3600 = 48"
Therefore: - 17.33° = - 17° 19'...


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