Find the area of the sector with an arc length of 2.5 feet and a radius of 20 inches. Round to the nearest square inch.
300 square inches
100
Find the exact value of cos 315 degrees using reference angles.
Square root of 2 /2
100
Find a, b, and c for the function f(x)=a sin(bx+c) such that the graph of f matches the figure below.
y = 2 sin (pi/2 x + pi/2)
where a =2, b = pi/2, c = pi/2
100
The length of a shadow of a tree is 125 feet when the angle of elevation of the sun is 33 degrees. Approximate the height of the tree to the nearest foot.
height of the tree is 81 feet
200
Convert -7pi/2 to degrees
-630 degrees
200
Find the area of the sector with radius 9 cm and an angle of 120 degrees. Round to the nearest hundredth.
84.82 square centimeters
200
Find two exact values of θ in degrees (0≤θ≤360°) if sin〖θ=-√3⁄2〗. Show work.
240 degrees and 300 degrees
200
Find a, b, and c for the function f(x)=a sin(bx+c) such that the graph of f matches the figure below.
y = 3 sin (2x + pi) or y = -3 sin (2x + 0)
200
A ladder 20 feet long leans against the side of a house. Find the height from the top of the ladder to the ground if the angle of the ladder is 80 degrees. Round to the nearest tenth of a foot.
19.7 feet
300
A rectangular window measures 54 inches by 24 inches. There is a 17-inch wiper blade attached by a 5-inch arm at the center of the base of the window. If the arm rotates 120 degrees, approximate the percentage of the window's area that is wiped by the blade.
37.1 percent
300
a. If s = 3 km and theta = 20 degrees, find the radius of the circle. Round to nearest hundredth.
b. Then find the area of the circle. Round to nearest hundredth.
a. 8.59 km
b. 12.88 square kilometers
300
Find two exact values of θ in degrees (0≤θ≤360°) if cos〖θ=-√2⁄2〗. Show work.
135 degrees and 225 degrees
300
Graph the equation y = 2 tan (1/2 x - pi). Find the period, amplitude, and phase shift. Sketch at least two cycles.
period = 2 pi, amplitude = 2, phase shift = 2 pi
300
A builder wishes to construct a ramp 24 feet long that rises to a height of 5.0 feet above level ground. Approximate the angle that the ramp should make with the horizontal. Round to the nearest degree.
12 degrees
400
Convert 3pi/10 from radians to degrees.
54 degrees
400
Sketch the angle 15pi/4 in standard position. Determine the quadrant in which the angle lies. Determine one positive and one negative coterminal angle in radians.
Quadrant IV
23pi/4, -pi/4
400
Find two values of θ in radians (0≤θ≤2π) if cscθ=1.1547. Round to the thousandths place.
1.047, 2.095
400
Graph the equation y = -4 cot (2 x - pi/2). Find the period, amplitude, and phase shift. Sketch at least two cycles.
period = pi/2, amplitude = 4, phase shift = pi/4
400
Trae is on the fourth floor of a burning building. The stairs are blocked and the elevator is not working. He finds a window whose base, he estimates, is 34 feet above the ground. He can see the fire truck through the window at an angle of depression of 42°. If the base of the ladder is 5 feet above the ground, how long must the ladder be extended to reach Trae?
43 feet
500
Convert 198.4 degrees to degrees, minutes, and seconds without using a calculator.
198 degrees 24 minutes 0 seconds
500
Sketch the angle -110 degrees in standard position. Determine the quadrant in which the angle lies. Determine one positive and one negative coterminal angle in degrees.
Quadrant III
250 degrees, -470 degrees
500
Given the indicated parts of triangle ABC with γ=90°, alpha = 12 degree 15 minutes, c = 430.5, approximate the remaining parts. Round to the nearest hundredth.
beta = 77 degrees 45 minutes, a = 91.34, b = 420.70
500
Graph the equation y = csc (2 x - pi/4). Find the period, amplitude, and phase shift. Sketch at least two cycles.
Claire stands at the top of a 100-feet-tall cliff. She spots a boat 600 feet off shore. What is the angle of elevation from the boat to Claire? Round to the nearest tenth.