Use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places. y = √5 − x (2, y) (x, 3)
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. csc 2π / 9
> Determine whether y is a function of x. x2 + y2 = 16
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. sec 12π / 5
> Test for symmetry with respect to each axis and to the origin. y2 = x3 − 8x
> You are in a boat 2 miles from the nearest point on the coast. You will travel to a point Q located 3 miles down the coast and 1 mile inland (see figure). You can row at 2 miles per hour and walk at 4 miles per hour. Write the total time T of the trip as
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. cot 401º
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. tan 33º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. tan 33º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. 405º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. -4π/3
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. 13π/6
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. 240º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. -45º
> Convert the radian measure to degree measure. -13π / 6
> Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. x2 + y2 = 4
> Find any intercepts. y = 4x2 + 3
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(t) = 2 / 7 + t
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
> Use a graphing utility to compare the graph of f(x) = 4/ π (sin πx + 1/3 sin 3 πx) with the given graph. Try to improve the approximation by adding a term to f(x). Use a graphing utility to verify that your new approximat
> The monthly sales S (in thousands of units) of a seasonal product are modeled by S = 58.3 + 32.5 cos πt/6 where t is the time (in months), with t = 1 corresponding to January. Use a graphing utility to graph the model for S and determine the months when
> The model for the height h of a Ferris wheel car is h = 51 + 50 sin 8πt where t is measured in minutes. (The Ferris wheel has a radius of 50 feet.) This model yields a height of 51 feet when t = 0. Alter the model so that the height of the car is 1 foot
> Sketch the graphs of f(x) = sin x, g(x) = │sin x│, and h(x) = sin(│x│). In general, how are the graphs of ∣f(x)∣ and f(∣x∣) related to the graph of f ?
> Consider an angle in standard position with r = 12 centimeters, as shown in the figure. Describe the changes in the values of x, y, sin θ, cos θ, and tan θ as θ increases continually from 0°
> How do the ranges of the cosine function and the secant function compare?
> Explain how to restrict the domain of the sine function so that it becomes a one-to-one function.
> You are given the value of tan θ. Is it possible to find the value of sec θ without finding the measure of θ? Explain.
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. g(x) = 1 / x2 + 2
> Find any intercepts. y = 2x – 5
> Find a, b, and c such that the graph of the function matches the graph in the figure. y = a sin(bx − c)
> Find a, b, and c such that the graph of the function matches the graph in the figure. y = a cos(bx − c)
> Sketch the graph of the function. y = 1 + sin(x + π/2)
> Sketch the graph of the function. y = 1 + cos(x – π/2)
> Sketch the graph of the function. y = cos(x – π/3)
> Sketch the graph of the function. y = sin(x + π)
> Sketch the graph of the function. y = csc 2πx
> Sketch the graph of the function. y = 2 sec 2x
> Sketch the graph of the function. y = tan 2x
> Sketch the graph of the function. y = csc x/2
> Use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places. y = x5 − 5x (−0.5, y) (x, −4)
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f (x) = x2 + 5
> Sketch the graph of the function. y = 2 tan x
> Sketch the graph of the function. y = -sin 2πx/3
> Sketch the graph of the function. y = sin x/2
> Sketch the graph of the function. y = sin x/2
> Use a graphing utility to graph each function f in the same viewing window for c = −2, c = −1, c = 1, and c = 2. Give a written description of the change in the graph caused by changing c. a. f(x) = sin x + c b. f(x) = -sin (2πx - c) c. f(x) = c cos x
> Use a graphing utility to graph each function f in the same viewing window for c = −2, c = −1, c = 1, and c = 2. Give a written description of the change in the graph caused by changing c. a. f(x) = c sin x b. f(x) = cos(cx) c. f(x) = cos(πx − c)
> Find the period of the function. y = csc 4x
> Find the period of the function. y = sec 5x
> Find the period of the function. y = 7 tan 2πx
> Find the period of the function. y = 5 tan 2x
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f (x) = 4 − x
> Determine the period and amplitude of each function. y = 2/3 cos πx/10
> Determine the period and amplitude of each function. y = −3 sin 4πx
> Determine the period and amplitude of each function. y = 3/2 cos x/2
> Determine the period and amplitude of each function. y = 2 sin 2x
> While traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 13 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of
> An airplane leaves the runway climbing at an angle of 18° with a speed of 275 feet per second (see figure). Find the altitude a of the plane after 1 minute.
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. cos θ/2 - cos θ = 1
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. cos2 θ + sin θ = 1
> Sketch the graph of the equation by point plotting. y = 1 / x + 2
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. sin θ = cos θ
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. sec θ csc θ = 2 csc θ
> Evaluate the function at the given value(s) of the independent variable. Then find the domain and range. a. f (−3) b. f (1) c. f (3) d. f (b2 + 1)
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. 2 cos2 θ –cos θ = 1
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. tan2 θ –tan θ = 0
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. tan2 θ = 3
> Solve the equation for θ, where 0 ≤ θ ≤ 2π. 2 sin2 θ = 1
> Find two solutions of each equation. Give your answers in radians (0 ≤ θ ≤ 2π). Do not use a calculator. a. sin θ = √3/2 b. sin θ = -√3/2
> Find two solutions of each equation. Give your answers in radians (0 ≤ θ ≤ 2π). Do not use a calculator. a. tan θ = 1 b. cot θ = -√3
> Find two solutions of each equation. Give your answers in radians (0 ≤ θ ≤ 2π). Do not use a calculator. a. sec θ = 2 b. sec θ = -2
> Sketch the graph of the equation by point plotting. y = 3/x
> Find two solutions of each equation. Give your answers in radians (0 ≤ θ ≤ 2π). Do not use a calculator. a. cos θ = √2/2 b. cos θ = -√2/2
> Determine the quadrant in which θ lies. a. sin θ > 0 and cos θ < 0 b. csc θ < 0 and tan θ > 0
> Determine the quadrant in which θ lies. a. sin θ < 0 and cos θ < 0 b. sec θ > 0 and cot θ < 0
> Evaluate the function at the given value(s) of the independent variable. Then find the domain and range. a. f (−2) b f (0) c. f (1) d. f (s2 + 2)
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. cot(1.35) b. tan(1.35)
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. tan π/9 b. tan 10π/9
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. sec 225° b. sec 135º
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. sin 10° b. csc 10º
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. 750º b. 510º c. 10π/3 d. 17π/3
> Sketch the graph of the equation by point plotting. y = √x + 2
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. 225º b. -225º c. 5π/3 d. 11π/6
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. -30º b. 150º c. -π/6 c. π/2
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. 60º b. 120º c. π/4 d. 5π/4
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. sec θ = 13/5
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. cos θ = 4/5
> Evaluate the function at the given value(s) of the independent variable. Then find the domain and range. a. f (−1) b. f (0) c. f (2) d. f (t2 + 1)
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. sin θ = 1/3
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. sin θ = 1/2
> Evaluate the six trigonometric functions of the angle θ. a. / b. /
> Evaluate the six trigonometric functions of the angle θ.
> Sketch the graph of the equation by point plotting. y = √x - 6
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f is a function, then f(ax) = af(x).
> A car is moving at the rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet. a. Find the number of revolutions per minute that the wheels are rotating. b. Find the angular speed of the wheels in radians per minute.
> Let r represent the radius of a circle, θ the central angle (measured in radians), and s the length of the arc subtended by the angle. Use the relationship s = rθ to complete the table.
> Convert the radian measure to degree measure. a. 7π / 3 b. –(11π / 30) c. 11π / 6 d. 0.438
> Convert the radian measure to degree measure. a. 3π / 2 b. 7π / 6 c. –(7π / 12) d. -2.367
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. a. -20º b. -240º c. -270º d. 144º
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. a. 30º b. 150º c. 315º d. 120º
> find the domain of the function. g(x) = 1 / │x2 - 4│
