Hi
Find sin q if q is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of the angle.
A -4/5
Ancient slingshots were made form straps of leather that cradled a rock until it was released. One would spin the slingshot in a circle, and the initial path of the released rock would be a straight line tangent to the circle at the point of release. The rock will travel the greatest distance if it is release when the angle between the normal to the path and the horizontal is -45. The center of the circular path is the origin and the radius of the circle measure 1.25 feet. Write and equation of the initial path of the rock in standard form.
A sqrt2x-sqrt2y-2.5=0
The escalator at St. Petersburg Metro in Russia has a vertical rise of 195.8 feet. If the angle of elevation of the escalator is 10 21 36 , find the length of the escalator.
B 1088.8ft
When a 757 passenger jet begins its descent to the Ronald Reagan National Airport in Washington, D.C., it is 3900 feet from the ground. Its angle of descent is 6 degrees How far must the plane fly to reach the runway?
B 37,310.4ft
Find the area of a sector with a central angle of 32 and a radius of 8.5 millimeters. Round to the nearest tenth.
C 20.2 mm^2
Carlos is making some observations from the roof of a building. Which angle is the angle of elevation from the car to Carlos?
C <PIK
Find tan q if q is an angle in standard position and the point with coordinates (4, 3) lies on the terminal side of the angle.
D 3/4
When a 757 passenger jet begins its descent to the Ronald Reagan National Airport in Washington, D.C., it is 3900 feet from the ground. Its angle of descent is 6 degrees What is the plane's ground distance to the airport?
D 37,106 ft
Sketch the angle to find its reference angle. 315 A 15 B 35 C 53 D 45
D 45
Carlos is making some observations from the roof of a building. Which angle is the angle of elevation from Carlos to the helicopter?
D LKM
Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?
D tan theta
Determining the normal form of the equation of a line is like finding the equation of a tangent line to a circle of radius p.
True
Find the value of the function sin 310. a. -0.766044443119 c. 0 b. 0.850887688656 d. 0.003225800857
a. -0.766044443119
Find the value of the function sin 9pi/7. a. -0.78 c. 0.96 b. 3.01 d. 0
a. -0.78
Use the unit circle to find sin 90. a. 1 c. -1 b. 0 d. undefined
a. 1
Find the value of the function sin 10pi/4. a. 1.00 c. 1.88 b. 0.60 d. 0
a. 1.00
The angle of depression from the top of the tree to the tip of the shadow is 25°. Find the height of the tree to the nearest tenth. a. 16.8 feet b. 18.2 feet c. 23.4 feet d. 39.7 feet
a. 16.8 feet
A 12-foot tree casts a 22-foot shadow. Find the angle of elevation from the tip of the shadow to the top of the tree. Round the answer to the nearest tenth. a. 28.6° b. 33.1° c. 56.9°d. 61.4°
a. 28.6
Kyle is pulled back on a swing so that the rope forms an angle of 30° with the vertical. The distance from the top of the swing set directly to the ground is 12 feet. Find Kyle's height off the ground, , when he is in the pulled-back position. Round the answer to the nearest hundredth. a. 3.34 feet b. 3.86 feet c. 8.56 feet d. 8.66 feet
a. 3.34 feet
Frank stands 450 feet from the base of the Statue of Liberty. If the Statue of Liberty is 306 feet tall, what is the angle of depression from the top of the statue's torch to Frank? Round the answer to the nearest tenth. a. 33.7° b. 34.2° c. 55.8° d. 56.3°
a. 33.7°
A 14-foot tree casts an 18-foot shadow. Find the angle of elevation from the tip of the shadow to the top of the tree. Round the answer to the nearest tenth. a. 37.9° b. 38.9° c. 51.1° d. term-1852.1°
a. 37.9°
Whitney starts the engine on her small private airplane. The engine drives a propeller with a radius of 6.5 feet and its centerline 10.5 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 850 revolutions per minute. The height of one propeller tip as a function of time is given by h = 10.5 + 6.5 sin(850t), where h is the height in feet and t is the time in minutes. Find h when t = 2 minutes. a. 4.1 ft b. 9.4 ft c. 16.9 ft d. 11.6 ft
a. 4.1 ft
According to the Americans with Disabilities Act, a ramp can rise no more than 1 ft for every 12 ft of horizontal distance. What is the maximum angle that the ramp can form with the ground? a. 4.8º c. 5.0º b. 2.7º d. 3.7º
a. 4.8º
Amy looks up to the 8-foot basketball hoop as shown. If the vertical distance from the ground to Amy's eyes is 5.9 feet, what is the angle of elevation from Amy to the hoop? Round the answer to the nearest tenth. a. 5.5º b. 14.1º c. 20.0º d. 84.5º
a. 5.5º
The Sears Tower in Chicago is 1454 feet high. Sketch and find the angle of elevation from a point 750 feet from the base to the top of the tower. Relate your answer to the nearest tenth. a. 62.7º b. 27.3º c. 31.1º d. 58.9º
a. 62.7º
Find the reference angle for 791° a. 71° c. 109° b. 161° d. 19°
a. 71°
Which trigonimetric function would you use to solve the problem? If t=55 and rt=5 find rs a. tan or cot c. cos or sec b. sin or csc d. sin or cos
a. tan or cot
Use the unit circle to find cos -270. a. 1 c. -1 b. 0 d. undefined
b. 0
Use the unit circle to find tan 360. a. 1 c. -1 b. 0 d. undefined
b. 0
For the given angle, find the coterminal angle such that -360° < q < 360°. -135° a. 45° c. -495° b. 225° d. -315°
b. 225°
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depression to the Groveburg soccer fields to be 15'. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 30'. The distance between the two athletic complexes is 4 miles. Find the distance from the balloon to the soccer fields. a. 3.2 mi c. 4.4 mi b. 3.6 mi d. 4.9 mi
b. 3.6 mi
A surveyor is standing 550 feet from the base of a redwood tree in the California Redwood Forest. The tree is 362 feet tall. Sketch a drawing that models the situation and then find the angle of elevation of the top of the tree from the spot where the surveyor is standing. a. 48.8o b. 33.4o c. 56.6o d. 41.0o
b. 33.4o
Find the angle with a tangent ratio of 0.9325. a. 77° c. 13° b. 43° d. 47°
b. 43°
Mae is checking her bicycle's wheel. The wheel has a radius of 28 cm, and its center is 42 cm above the ground. Mae is rotating the wheel at a constant speed of 190°/s. The height of a point on the tire as a function of time is given by h = 42 + 28 sin(190t), where h is the height in centimeters and t is the time in seconds. Find h when t = 2 s. Find your answer to the nearest tenth of a centimeter. a. 52.0 sm b. 51.6 cm c. 51.5 cm d. 50.0 cm
b. 51.6 cm
Using a scientific calculator or graphing calculator to find the inverse tangent of the ratio. Round to the nearest degree. 7/5 a. 36° b. 54° c. 46° d. 44°
b. 54°
Find the reference angle for -72° a. -18° c. 108° b. 72° d. -108°
b. 72°
Find sin^-1 0.9563 to the nearest degree. a. 17° c. 28° b. 73° d. 13°
b. 73°
Which of the following statements is true? a. The angle of elevation is always greater than the angle of depression. b. The angle of elevation is always the line of sight above the horizontal. c. The angle of elevation is always less than the angle of depression. d. The angle of depression is always the line of sight above the horizontal.
b. The angle of elevation is always the line of sight above the horizontal.
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depression to the Groveburg soccer fields to be 20° 15'. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62° 30'. The distance between the two athletic complexes is 4 miles. What is the distance from the balloon to the football field? a. 3.6 mi c. 6.2 mi b. 2.2mi d. 1.4 mi
d. 1.4 mi
A mini toy helicopter ascends 50 feet vertically, then flies horizontally 200 feet. Find the angle of elevation to the helicopter now as seen by an observer at the takeoff point. Round to the nearest degree. a. 75º b. 15º c. 76º d. 14º
d. 14º
If the measurement of a central angle is 5pi/6 find the length of its intercepted arc in a circle with a radius of 15 inches. a. 33.4 inches c. 37.5 inches b. 35.6 inches d. 39.3 inches
d. 39.3 inches
Find the reference angle for 497° a. 137° c. 47° b. 133° d. 43°
d. 43°
A hiker standing at point G wants to estimate the distance across the lake to point H, which is directly north of her location. She walks 650 feet west to point F. She measures the angle from point F to point H to be 84º north of east. Find the distance across the lake to the nearest tenth of a foot. a. 68.3 feet b. 646.4 feet c. 655.4 feet d. 6,184.4 feet
d. 6,184.4 feet
A 12-foot tree casts a 22-foot shadow. Find the angle of elevation from the tip of the shadow to the top of the tree. Round the answer to the nearest tenth. a. 28.6° b. 33.1° c. 56.9° d. 61.4°
d. 61.4°
The angle of depression from the basketball hoop to Claire's eyes is 9.2°. The vertical distance from the ground to Claire's eyes is 5.6 feet. Using the diagram, find the height of the basketball hoop to the nearest tenth. a. 3.5 feet b. 3.6 feet c. 9.1 feet d. 9.2 feet
d. 9.2 feet
A coterminal angle is the positive acute angle formed by the terminal side of q and the nearest part of the x-axis.
false
The motion of a ship riding at anchor can be modeled by y = 22 + 4 cos , where y is the water depth in feet and t is the time in hours. Consider a day in which t = 0 represents 12:00 midnight. At what time during that day will the water under the ship be the deepest and what time will it be the shallowest? What will the water's depth be at these times? a. deepest at 6:00 a.m. and 6:00 p.m., depth 26 ft shallowest at 12:00 noon and 12:00 midnight, depth 18 ft b. deepest at 12:00 noon and 12:00 midnight, depth 26 ft shallowest at 6:00 a.m. and 6:00 p.m., depth 18 ft c. deepest at 12:00 noon and 12:00 midnight, depth 21 ft shallowest at 6:00 a.m. and 6:00 p.m., depth 29 ft d. deepest at 6:00 a.m. and 6:00 p.m., depth 29 ft shallowest at 12:00 noon and 12:00 midnight, depth 21 ft
b. deepest at 12:00 noon and 12:00 midnight, depth 26 ft shallowest at 6:00 a.m. and 6:00 p.m., depth 18 ft
Which trigonimetric function would you use to solve the problem? If s=27 and tr=7 find ts a. tan or cot c. cos or sec b. sin or csc d. sin or cos
b. sin or csc
Use the unit circle to find csc 270. a. 1 c. -1 b. 0 d. undefined
c. -1
For the given angle, find the coterminal angle such that -360° < q < 360°. 90° a. 90° c. -270° b. 270° d. -90°
c. -270°
Kahleela starts the engine on her small private airplane. The engine drives a propeller with a radius of 8.5 feet and its centerline 11.5 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 800 revolutions per minute. The height of one propeller tip as a function of time is given by h = 11.5 + 8.5 sin(800t), where h is the height in feet and t is the time in minutes. Find h when t = 5.5 minutes. a. 3.1 ft b. 13 ft c. 19.9 ft d. 10 ft
c. 19.9 ft
Find cos^-1 0.9455 to the nearest degree a. 26° c. 19° b. 71° d. 41°
c. 19°
If the measurement of a central angle is 77 find the length of its intercepted arc in a circle with a radius of 15 inches. a. 18.4 inches c. 20.2 inches b. 16.6 inches d. 22.6 inches
c. 20.2 inches
Find the reference angle for 697° a. 67° c. 23° b. 157° d. 113°
c. 23°
An ant looks up to the top of a tree at an angle of elevation of . If the ant is 30 feet from the base of the tree, what is the height of the tree, to the nearest tenth? a. 19.3 feet b. 23.0 feet c. 25.2 feet d. 35.8 feet
c. 25.2 feet
A ship's sonar detects a submarine 880 feet below a point on the ocean's surface 1450 ft dead ahead of the ship. To the nearest degree, find the angle x. a. 59º b. 37º c. 31º d. 53º
c. 31º
Keenan is checking his bicycle's wheel. The wheel has a radius of 21 cm, and its center is 56 cm above the ground. Keenan is rotating the wheel at a constant speed of 165°/s. The height of a point on the tire as a function of time is given by h = 56 + 21 sin(165t), where h is the height in centimeters and t is the time in seconds. Find h when t = 17 s. Round your answer to the nearest tenth of a centimeter. a. 35.5 sm b. 36.0 cm c. 35.7 cm d. 36.7 cm
c. 35.7 cm
The angle of elevation from the tip of the shadow to the top of the tree is 36°. Find the distance from the top of the tree to the tip of the shadow. Round the answer to the nearest tenth. a. 26.7 feet b. 30.2 feet c. 40.8 feet d. 42.9 feet
c. 40.8 feet
From the top of a tree, a bird looks down on a field mouse at an angle of depression of 50°. If the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes. Round the answer to the nearest tenth. a. 33.6 m b. 42.0 m c. 47.7 m d. 59.6 m
c. 47.7 m
Which is NOT an example of the three trigonometric reciprocals of sine, cosine and tangent? a. cosecant c. theorem b. secant d. cotangent
c. theorem
Find the value of the function sin 550. a. 0 c. 0.001818180816 b. -0.21948407741 d. -0.173648177667
d. -0.173648177667
Find the value of the function sin 7pi/2 . a. -1.10 c. 0 b. -0.35 d. -1.00
d. -1.00
Change -1.75 to degree measure & round to the nearest tenth. a. -99.3 c. -101.5 b. -96.5 d. -100.3
d. -100.3
Find tan A for the triangle below. a. 0.868 b. 0.496 c. 1.75 d. 0.5714
d. 0.5714
