Trigonometry

  1. If the radius of a pizza is 20 cm, what is the central angle in degrees that gives one person 30 cm of crust?

    Question 5 options: a) 120° b) 35° c) 43° d) 86° I say option a, but my partner disagrees

  2. If a point on the Cartesian plane lies at (4, 2), what is the angle made between the line containing the point and the origin, and the negative y-axis?

    a) 1.249 radians b) 0.463 radians c) 0.523 radians d) 1.047 radians

  3. A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 2 feet above the ground. The horizontal distance from the bottom of the ramp to the building is 15 feet. What is the angle of elevation of the ramp to

  4. At t = 0 a car is due 2 km north of you heading west moving 13 km/s after 1.5 s. What is the angle in radians between you and the car from where the car was at t = 0?

  5. A batter hits a ball with an initial velocity v0 of 100 feet per second at an angle theta to the horizontal. An outfielder catches the ball 200 feet from home plate. Find theta if the range of a projectile is given by the formula R=1/32v0 squared times sin

  6. Hello!

    Explain why the primary trigonometric ratios depend only on the given angle and not the size of legs and hypotenuse of a right triangle? I am not 100% sure but it is because the angles have the same value for all of the ratios? Is it also because the

  7. If k = 2π/45, what is the period?

  8. If the central angle is 4pi/3 radians, what should the radius of a circle be to make the arc length 1 m?

    a) 0.424 m b) 0.238 m c) 2.356 m d) 4.188 m I think it is c)... is that correct?

  9. A painter needs to cover a triangular region 62 meters by 68 meters by 70 meters. A can of paint covers 70 square meters. How many cans will be needed?

  10. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.

    The adjacent is 12cm wide and the angle of the hypotenuse is at 35 degrees. The opposite is x. I'm posting this here because I want to know what I did wrong regarding my

  11. A plane leaves airport A and travels 560 miles to airport B at a bearing of N32E. The plane leaves airport B and travels to airport C 320 miles away at a bearing of S72E. Find the distance from airport A to airport C.

  12. Use a graph of the function to approximate the solution of the equation on the interval

    [−2π, 2π]. (List the solutions in increasing order from left to right on the x-axis. Round your answers to three decimal places.) cot x = −1

  13. solve 2tanx cos2x+1=tan3x+2cos2x

  14. A lean-to is a simple shelter with three walls, a sloping roof, and an open front facing away from the prevailing winds. The back wall is short compared to the front opening. If the lean-to at a campsite has a front opening that is 7.0 ft tall, a back wall

  15. Two observers who are 2 miles apart on a horizontal plane observe a balloon in a same vertical plane with themselves. the angles of elevation are 50 degrees and 65 degrees respectively. find the height of the balloon,(a)if it is between the observers;(b)if

  16. The graph of y=tan x has vertical asymptotes at certain values of x because the tangent ratio is _____ at those values.

    a) vertical b) undefined c) zero d) intermediate I believe it's a), but I am not too sure.

  17. The length of one of the sides of a triangle is equal to 1m, the measurement of adjacent angles are 30º and 45º. What are the lengths of the other sides of this triangle?

  18. Points A and B 1000 meter apart are plotted on a straight highway running east and west. from A, the bearing of tower C is N32*W and from be, the bearing of C is N64*E. approximate the shortest distance of the tower from the highway.

    please explain........

  19. How do you verify the equation is an identity?

    Tan^2x-tan^2y=sec^2x-sec^2y and, how do you factor and simplify, cscx(sin^2x+cos^2xtanx)/sinx+cosx

  20. (Triangle ABC is scalene) AC is a straight shore line and B is a boat out at sea. Angle A is 60 degrees and Angle C is 45 degrees. Find the shortest distance from the boat to the shore if A and C are 5km apart...I honestly have no idea where to start with

  21. A bridge across a valley is 150 m in

    length. The valley walls make angles of 60° and 54° with the bridge that spans it, as shown. How deep is the valley, to the nearest metre?

  22. Prove identity.

    Sec(pi-x)=-sec x

  23. Write the expression as a trigonometric function of only θ, and use a graphing utility to confirm your answer graphically.

    cos((9π/2)-θ

  24. Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)

    sin(x + π) − sin x + sqrt(3)=0

  25. If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70o to 60o, what is the height of the building?

  26. Find all solutions of the equation in the interval [0,2pi).

    sec(theta)+2=0 Write your answer in radians in terms of pi

  27. A 40 foot ladder which is leaning against a wall reaches a wall at a point 36 feet above the ground. Find the measure of angle created between the ladder and the ground.

  28. Triangle ABC is a right triangle with right angle at C. CD is perpendicular to AB. BC=4 and CD=1. find the area of the triangle ABC.

  29. AN AIRPLANE IS FLYING AT A HEIGHT OF 1000 m. THE ANGLE OF DEPRESSION OF AIRPORT A FROM THE PLANE IS 15°. CALCULATE THE HORIZONTAL DISTANCE BETWEEN THE AIRPLANE AND THE AIRPORT.

  30. 2cos^2(x) = 13sinx - 5

    How do i solve for x? I think i have to use the sin^2x + cos^2x = 1, but I'm not sure how to use that. I thought about maybe doing 2(1-sin^2x) = 13sinx - 5 but then i get stuck. Any suggestions?

  31. Surveying

    A surveyor wishes to find the distance across a swamp. The bearing from A to B (Segment AB is opposite side of triangle) is N 32° W. The surveyor walks 50 meters from A to C, and at the point C the bearing to B is N 68° W. (Segment AC is

  32. A vertical pole 40 feet tall stands on a hillside that makes an angle of 17 degrees with the horizontal. Approximate the minimum length of cable that will reach the top of the pole from a point on the hillside 72 feet downhill from the base of the

  33. find sin2x, cos2x, and tan2x if sinx= -2/sqrt 5 and x terminates in quadrant III

  34. Two sides of a right triangle are 8, 15 and 17 units. if each side is doubled, how many sqare units will the area of the new triangle be?

  35. Stumped on this question - please explain!

    If sin A = 0.35, cos A = 0.94, sin B = 0.58, and cos B = 0.81, what is sin(A + B)? Am I just plugging the values into sin(A + B) or do I have to do more than that? Thank you.

  36. A cat, sitting on top of a tree, spots a dog and a firefighter, both on flat ground below. From the cat's point of view, the dog is 10m south, at an angle of depression of 65 degrees, and the firefighter is some distance east of the tree, at an angle of

  37. Find all solutions between 0 and 2pi. Round to two decimal places. In radians.

    Find all solutions between 0 and 2 pi. Round to two decimal places for the final solutions. The answers should be in radian mode. If you can use exact values use them. At least

  38. A translation maps (-6,2) onto (-4,-2). Find the image of (3,5) under the same translation.

  39. prove that [(sin 2 t / sin t )] - [( cos 2t ) / cos t ] = sec t

    and sin (2t - t ) = sin t

  40. The wheelchair ramp is 4.4 m long. It rises 1.2 m. What is its angle of inclination to the nearest degree?

  41. If someone could tell me if this is correct, it would really help me out.

    Problem: A statue 20 feet high stands on top of a base. From a point in front of the statue, the angle of elevation to the top of the statue is 48 degrees, and the angle of elevation

  42. Find all solutions of 4 (cos (x)**2)-1=0 in the interval (6pi, 8pi).

    (Leave your answers in exact form and enter them as a comma-separated list.)

  43. Factor 1-sin^3x

  44. If sin(x) = 4cos(x), then what is (sin(x))*(cos (x))?

  45. Given the trigonometric function y = tan x, find the x-coordinate of the point (3pi/4, ?)

    a) -1 b) root 2 c) c d) 1/root 2

  46. a bicycle with 24inch diameter wheels is traveling at 15mi/hr.

    a) Find the angular speed of the wheels in rad/min. b)How many revolutions per minute do the wheels make?

  47. A ladder 5 meter long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with the ground. how high up the wall does it reach?

  48. a flagpole 25 feet tall stands on a top of a building. from a point in the same horizontal plane with the base of the building. The angle of elevation of the top and the bottom are 61°30' and 56°20' respectively. How high is the building?

  49. 4. An observer is near a river and wants to calculate the distance across the river. He measures the angle between his observations of two points on the shore, one on his side and one on the other side, to be 28º. The distance between him and the point on

  50. Solve the equation. (Find all solutions of the equation in the interval [0, 2π). Enter your answers as a comma-separated list.)

    4 tan(2x) − 4 cot(x) = 0

  51. To unload hollow blocks from a cargo truck a wooden plank whose end rests against the truck’s flat-form 1.5 meters above the ground is used. If it is inclined 37 degrees 49 minutes with the ground, how long is the wooden plank?

  52. two airplanes leave an airport at the same time one hour later they are 189km/hr apart. if one plane traveled 168km/hr and the other traveled 244km/hr for the hour what is the angle between their flight path

  53. Verify the identity algebraically.

    TAN X + COT Y/TAN X COT Y= TAN Y + COT X

  54. over which of the following domains is f(x) = csc(0.1x + 1.2) defined at all points and invertible?

    x = [0,10] x = [10,20] x = [20,30] x = [30,40] Can someone please explain how to solve this to me and show me all the steps rather than simply giving me the

  55. The wheels of a scooter have a diameter of 4.5 inches. If the person riding the scooter is traveling down hill at 15.0 mph. what is the approximate angular speed of the wheels in radians per second

  56. How do I find the value of sin(a-b) if tana=4/3, cotb=5/12, 0<a<90, and 0<b<90?

  57. Determine the number of triangles ABC possible with the given parts.

    b=60 a=82 B=100

  58. Hi! The question is really confusing to me. I can't sketch/visualize the problem. :(

    From a given position an observer notes that the angle of elevation of a rock is 47 degrees. After walking 1000 feet towards the rock, up a slope of 32 degrees, he finds

  59. A building 200 feet tall casts an 80 ft long shadow. If a person looks down from the top of the building which of the following is the measure of the angle between the end of the shadow and the vertical side of the building to the nearest degree? I

  60. The hypotenuse of a right triangle is 34cm. find the length of the two legs, if one leg is 14cm longer than the other.

  61. Given that sin^2x = 4/13, what is the cos^2x?

    I am so lost. I need to show my work. Please help. THANK YOU!

  62. point A and B are 100m apart and are of the same as the foot of a building. the angle of elevation of the top of the building from point A an B are 21 degrees and 32 degree respectively. how far is A from the building

  63. An airplane is sighted at the same time by two ground observers who are 2 miles apart and both directly west of the airplane. They report the angles of elevation as 11˚ and 20˚. How high is the airplane? Round to the nearest hundredth of a mile.

  64. Find the diameter of a pulley which is driven at 360 rpm by a belt moving at 40 ft/s.

    Then in 1 s the pulley turns through an angle theta measuring 12 pi radians and a point on the rim travels a distance s= 40 ft.

  65. change 8 cis 240 degrees to rectangular form

  66. Find all degree solutions. (Enter your answers as a comma-separated list. Let k be any integer.)

    2 cos2 6θ + 3 cos 6θ + 1 = 0

  67. The expression log(x^n/ radical y)is equivalent to

    1. n log x - 1/2 log y 2. n log x- 2 log y 3. log (nx) - log (1/2y) 4. log (nx) - log (2y)

  68. A plane is observed approaching your home and you assume its speed to be 550 miles per hour. The angle of elevation of the plane is 16 degrees and one minute later is 57 degrees. Approximate the altitude of the plane.

    Draw yourself a figure with two

  69. Two sides of a triangle are 5 and 8 units respectively. If the included angle is changing at rate of one radian, at what rate is the third side changing when the included angle is 60 degrees?

  70. The perimeter of an isosceles triangle is 6.6824. find its area.

  71. A sine function has an amplitude of 4/7, period of 2pi, horizontal shift of -3pi, and vertical shift of 1. 

    What is the y-value of the positive function at x= pi/2? 

  72. which of the following is a solution for the equation 1/485 tan^2x=0

    a) no solution b) 485 pi c) pi d) pi/2 I'm getting conflicting answers when I try to solve it.

  73. Someone please help!!!?

    7. What is 1/cot(x) in terms of sine? This is what I've got so far: sin = 1/csc tan = 1/cot 1+cot2(x) = csc2(x) 1/1+cot2(x) = 1/csc2(x)

  74. A helicopter hovers 1000 feet above the end of a lake. If the angle from the helicopter down to the other end of the lake 32°24’, find the length of the lake.

  75. A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 58°. A guy wire is to be attached to the top of the tower and to the ground, 50 m downhill from the base of the tower. The angle α in the

  76. If A + B + C = 180°, Prove that

    Cos²A + Cos²B + Cos²C = 1-2cosAcosBcosC

  77. Let (7,-3) be a point on the terminal side of theta. Find the exact values of cos of theta, sec of theta and cot of theta?

  78. State the quadrant in which theta lies.

    sin(theta) > 0 and cos(theta) > 0 How can I determine this? Please explain.

  79. The populations, P, of six towns with time t in years are given by:

    I) P=1000(1.08)^t II) P= 600(1.12)^t III) P = 2500(0.9)^t IV) P=1200(1.185)^t V) P=800(0.78)^t VI) P=2000(0.99)^t a. Which towns are growing in size? Which are shrinking? b. Which town is

  80. If the terminal side of angle theta passes through point (-3, -4), what is the valuse of sec theta?

    1) 5/3 2) -5/3 3)5/4 4)-5/4

  81. Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30o. The balloon rises 50 meters. Now the angle of depression to the car is 35°. How far is the car

  82. An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4° and 6.5°. How far apart are the ships?

  83. An elliptical arch is constructed which is 6 feet wide at the base and 9 feet tall in the middle. Find the height of the arch exactly 1 foot in from the base of the arch. looking for direction with what ellipse equation is and how to approach this problem

  84. A passenger in an airplane flying at an altitude of 10 kilometers sees two towns directly to the left of the plane. The angles of depression to the towns are 28° and 55°. How far apart are the towns?

  85. Mountain officials want to build a new ski lift from B to C as shown in the figure below. The distance from A to C is 1480 feet. They measure angle DAC to be 32 degrees and angle DBC to be 18 degrees. What is the distance A from to B? Round your answer to

  86. Prove that

    cos(A+B) + sin(A-B) = 2sin(45°+A)cos(45°+B)

  87. This is a logs question

    If u=x/y^2, which expression is equivalent to log u? 1) log x + 2 log y 2) 2(log x- log y) 3) 2(log x + log y) 4) log x- 2 log y

  88. A plane is 160 miles north and 85 miles east of an airport. If the pilot wants to fly directly to the airport, what bearing would be taken?

  89. a boat travels on a course of bearing n 37 10' W for 79.5 miles. How many miles north and how many miles west has the boat traveled?

  90. A vertical pole 35m high, standing on sloping ground is braced by a wire which extends from the top of the pole to a point on the ground 25 m from the foot of the pole. If the pole subtends an angle of 30 degrees at the point where the wire reaches the

  91. 4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant.

    5. Find the exact value for cos 165degrees using the half-angle identity. 1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0 less than or equal to x <2pi.

  92. A Ferris Wheel rotates 3 times each minute. The passengers sit in seats that are 25 feet from the center of the wheel.

    A. What is the angular velocity of the wheel in degrees per minute and radians per minute? B. What is the linear velocity of the passenger

  93. Angle x is a third quadrant angle such that cos x = -(2/3).

    What is the exact value of cos (x/2) ? Solve in simplest radical form.

  94. How do I find all solutions to:

    tanx+3cotx=4? The answer choices are: a.) x=arctan3+nPi b.) x=arccot3+nPi

  95. A 19-ft ladder leans against a building so that the angle between the ground and the ladder is 80∘.

    How high does the ladder reach on the building? I did 19sin(80) to get me 18.76847847 for how high the ladder reach on the building... but when i put the

  96. 1. 4sin^2x=3tan^2x-1

    2. 8cos^2x-4cos^4x=3 3. 3secx-cosx=2

  97. a rope dancer was walking on a loose roop tied to the top of two equal post of height 9m. when he was 3m above the ground, it was found that stretched pieces of roop made angle of 30 degree and 60 degree with the horizontal line parallel to the ground.

  98. If sinA + sinB = a and cosA + cosB = b, find the value of tanA-B/2

  99. Having trouble with true/false questions in Trigonometry. They read as follows -

    True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then x=f^-1(y). Explain your answer.

  100. a 30 feet ladder resting against a building makes a 60 angle with the ground . find the Height from the ground at which the ladder touches the building to the nearest foot

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