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mathematics
precalculus

Questions and Answers of Precalculus

The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.y = tan xy = 1
The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.y = 2 sin xy = -2
The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.y = cos xy = 1/2
The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.y = sin xy = 1/2
Graph y = |sin x|, -2π ≤ x ≤ 2π
Graph y = |cos x|, -2π ≤ x ≤ 2π.
Biorhythms In the theory of biorhythms, a sine function of the formP(t) = 50 sin(ωt) + 50is used to measure the percent P of a person's potential at time t, where t is measured in days and t = 0 is
A one-lane highway runs through a tunnel in the shape of one-half a sine curve cycle. The opening is 28 feet wide at road level and is 15 feet tall at its highest point.(a) Find an equation for the
The voltage V produced by an ac generator is sinusoidal. As a function of time, the voltage V isV(t) = V0 sin(2π ft)where f is the frequency, the number of complete oscillations (cycles) per second.
The voltage V, in volts, produced by an ac generator at time t, in seconds, is(a) What is the amplitude? What is the period?(b) Graph V over two periods, beginning at t = 0.(c) If a resistance of R =
Find an equation for graph. -4т -2п 10пх 2т 6п
Find an equation for graph. УА 6 8 10 x -4 -2 2 -5-
The voltage V, in volts, produced by an ac generator at time t, in seconds, isV(t) = 220 sin(120πt)(a) What is the amplitude? What is the period?(b) Graph V over two periods, beginning at t = 0.(c)
The current I, in amperes, flowing through an ac (alternating current) circuit at time t in seconds, isI(t) = 120 sin(30πt) t ≥ 0What is the period? What is the amplitude? Graph this function over
The current I, in amperes, flowing through an ac (alternating current) circuit at time t in seconds, isI(t) = 220 sin(60π) t ≥ 0What is the period? What is the amplitude? Graph this function over
Find the average rate of change of f from 0 to π/2.f(x) = cos(2x)
Find the average rate of change of f from 0 to π/2.f(x) = sin(x/2)
Find the average rate of change of f from 0 to π/2.f(x) = cos x
Find the average rate of change of f from 0 to π/2.f(x) = sin x
Find an equation for graph. 4 -4
Find an equation for graph. 3 -4 4,
Find an equation for graph. -2 -2 2. 2.
Find an equation for graph. 3 -2 6 -3
Find an equation for graph. 2т 2п 4п 3 3
Find an equation for graph. Уд 2 m/2
Find an equation for graph. т 2т п TT
Find an equation for graph. Уд 2п 2п 4т -1 3 3
Find an equation for graph. 2
Find an equation for graph. হ োক
Find an equation for graph. 2 3 -2- 4)
Find an equation for graph. У ЗН -2 т 2т 4т
A neighborhood carnival has a Ferris wheel whose radius is 30 feet.You measure the time it takes for one revolution to be 70 seconds.What is the linear speed (in feet per second) of this Ferris
Pulleys Two pulleys, one with radius 2 inches and the other with radius 8 inches, are connected by a belt. (See the figure.) If the 2-inch pulley is caused to rotate at 3 revolutions per minute,
Speed of Earth The mean distance of Earth from the Sun is 9.29 × 107 miles. Assuming that the orbit of Earth around the Sun is circular and that 1 revolution takes 365 days, find the linear speed of
Speed of the Moon The mean distance of the moon from Earth is 2.39 × 105 miles. Assuming that the orbit of the moon around Earth is circular and that 1 revolution takes 27.3 days, find the linear
Linear Speed on Earth Earth rotates on an axis through its poles. The distance from the axis to a location on Earth 400 north latitude is about 3033.5 miles. Therefore, a location on Earth at 40°
Linear Speed on Earth Earth rotates on an axis through its poles. The distance from the axis to a location on Earth 300 north latitude is about 3429.5 miles. Therefore, a location on Earth at 300
Distance between Cities Charleston, West Virginia, is due north of Jacksonville, Florida. Find the distance between Charleston (38°21' north latitude) and Jacksonville (30°20' north latitude).
Distance between Cities Memphis, Tennessee, is due north of New Orleans, Louisiana. Find the distance between Memphis (35°9' north latitude) and New Orleans (29°57' north latitude). Assume that the
The radius of each wheel of a car is 15 inches. If the wheels are turning at the rate of 3 revolutions per second, how fast is the car moving? Express your answer in inches per second and in miles
The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 35 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning? molyetat
An object is traveling around a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters, what is its angular speed? What is its linear speed?
An object is traveling around a circle with a radius of 5 centimeters. If in 20 seconds a central angle 1/3 of radian is swept out, what is the angular speed of the object? What is its linear speed?
A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places.r = 2 inches, θ = 30°, A = ?
A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places.r = 3 meters, θ = 120°, A = ?
A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places.r = 6 meters, A = 8 square meters, θ = ?
A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places.r = 5 miles, A = 3 square miles, θ = ?
In problem, A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places.θ = 1/4 radian, A = 6 square
In problem, A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places.θ = 1/3 radian, A = 2 square
A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places.r = 6 feet, θ = 2 radians, A = ?
Match the given function to one of the graphs (A)–(D). y = -3 sin 2° 3 3 3 8т 2 2T 8т -3 -3 -3 -3 (A) (B) (C) (D)
Match the given function to one of the graphs (A)–(D).y = 3 sin(2x) 3 3 3 8т 2 2T 8т -3 -3 -3 -3 (A) (B) (C) (D)
Match the given function to one of the graphs (A)–(D).y = -3 sin(2x) 3 3 3 8т 2 2T 8т -3 -3 -3 -3 (A) (B) (C) (D)
Match the given function to one of the graphs (A)–(J).y = 3 sin(2x) УА УА УА 2 -2 /4п -2 -2T 4п 4п -2 (B) (A) (C) УА y. 2 for -2T/ 3 4 3 4 5 2 Зп 5т X 5 X TT -2 (D) (E) (F) y. 3
Match the given function to one of the graphs (A)–(J). y = 2 sin УА УА УА 2 -2 4п -2 /4п -2T 4п -2 (A) (B) (C) УА y. 2 for -2T/ Зп 5т X 3 4 5 2 3 4 5 X TT -2 (D) (E) (F) y. 3 У y. 3
Determine the amplitude and period of each function without graphing. 3. cos Cos x y =
Find the exact value of each of the remaining trigonometric functions of θ. 2 3' sin 0 = 2
Find the exact value of each of the remaining trigonometric functions of θ. cos8= 3 Solve for sin sin0+ cos 0 = 1 : tan 8 = csc 8= sec 8= Since is in quadrant II, sin > 0. sin 0 =1-cos0 cot 8 = I
Find the exact value of each of the remaining trigonometric functions of θ. cos 0 = 4 + lin 5' 270 < < 360
Find the exact value of each of the remaining trigonometric functions of θ. sin 0 = 5 13' 90 0 180
Find the exact value of each of the remaining trigonometric functions of θ.sin θ = -5/13, θ in quadrant III
Find the exact value of each of the remaining trigonometric functions of θ.cos θ = -4/5, θ in quadrant III
Find the exact value of each of the remaining trigonometric functions of θ.cos θ = 5/3, θ in quadrant IV
In problem, find the exact value of each of the remaining trigonometric functions of θ.sin θ = 12/13, θ in quadrant II
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. sin 0 2 cos e 3 3
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. sin 0 21 cos e 3' 3
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. V3 sin 0 = 2 cos e 2
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. V3 sin 2' cos e = 2 2.
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. V5 2V5 5 sin 0 cos e
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. V5 sin 0 cos e 5. 5.
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. 4 sin 0 5' 5 cos e in
In problem, sin θ and cos θ are given. Find the exact value of each of the four remaining trigonometric functions. 3 cos e 4 sin 0 = 5'
Name the quadrant in which the angle θ lies.csc θ > 0, cos θ < 0
Name the quadrant in which the angle θ lies.sec θ < 0, sin θ > 0
Name the quadrant in which the angle θ lies.cos θ < 0, tan θ > 0
Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.cot 17π/4
Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.tan 405°
Show that the period of f(θ) = cot θ is π.
Is the cosine function even, odd, or neither? Is its graph symmetric? With respect to what?
Is the sine function even, odd, or neither? Is its graph symmetric? With respect to what?
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.cos(-π/4)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.sin(-π)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.tan(-π/4)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.cos(-270°)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.sin(-90°)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.csc(-30°)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.sec(-60°)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.sin(-135°)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.tan(-30°)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.cos(-30°)
Use the even–odd properties to find the exact value of each expression. Do not use a calculator.sin(-60°)
Find the exact value of each of the remaining trigonometric functions of θ.sec θ = -2, tan θ > 0
Find the exact value of each of the remaining trigonometric functions of θ. tan 0 = 3 sin e > 0 0
Find the exact value of each of the remaining trigonometric functions of θ. cot 0 = 4 3' cos 0 0
Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. Зт 5 х 2 2 cos 5
Find the exact value of each of the remaining trigonometric functions of θ. tan 0 = 3 4' sin 0 < 0
Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. 5 3 2т - х 3 sin y =
Find the exact value of each of the remaining trigonometric functions of θ.csc θ = 3, cot θ < 0
Find the exact value of each of the remaining trigonometric functions of θ.sec θ = 2, sin θ < 0
GraphDo you think that y = tan x and y = -cot x + 2 TT tan x = -cot x +

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