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mathematics
algebra and trigonometry graphs

Questions and Answers of Algebra And Trigonometry Graphs

For the given angle of rotation and coordinates of a point in the x′y′-coordinate system, find the coordinates of the point in the xy-coordinate system.θ = 60°, ( -1, -√3)
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
Find an equation of the ellipse having vertices (0, -5) and (0, 5) and with minor axis of length 4.
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
Using a parametric graph of the unit circle, find the function value. TT sin 4
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
For each equation:a) Tell whether the equation describes a parabola, an ellipse, or a hyperbola.b) State whether the directrix is vertical or horizontal and give its location in relation to the
GraphState whether the directrix s vertical or horizontal, describe its location in relation to the pole, and find the vertex or vertices. r = 2 1 - sin 0
Using a parametric graph of the unit circle, find the function value. COS 17 T 12
Using a parametric graph of the unit circle, find the function value. 2πT COS 3
Using a parametric graph of the unit circle, find the function value. sin 4T 5
Using a parametric graph of the unit circle, find the function value. πT tan 5
Graph: 5x2 - 8xy + 5y2 = 9.
Using a parametric graph of the unit circle, find the function value. tan 2π 7
Find a polar equation of the conic with a focus at the pole, eccentricity 2, and directrix r = 3 sec θ.
Graph the plane curve given by the parametric equationsx = √t, y = t + 2; 0 ≤ t ≤ 16.
The sum of two numbers is 1 and the sum of their squares is 13. Find the numbers.
Find a rectangular equation equivalent to x = 3 cos θ, y = 3 sin θ; 0 ≤ θ ≤ 2π.
Find two sets of parametric equations for the rectangular equation y = x - 5.
Using a parametric graph of the unit circle, find the function value.cos 5.29
A projectile is launched from a height of 10 ft with an initial speed of 250 ft/sec at an angle of 30° with the horizontal.a) Find parametric equations that give the position of the projectile at
Is a parabola always the graph of a function? Why or why not?
Using a parametric graph of the unit circle, find the function value.sin 1.83
Find two sets of parametric equations for the rectangular equation.y = 4x - 3
Is the center of an ellipse part of the graph of the ellipse? Why or why not?
Find two sets of parametric equations for the rectangular equation.y = x2 - 1
What would you say to a classmate who tells you that it is always possible to visualize all the solutions of a nonlinear system of equations?
Find two sets of parametric equations for the rectangular equation.y = (x - 2)2 - 6x
Find two sets of parametric equations for the rectangular equation.y = x3 + 3
A ball is thrown from a height of 7 ft with an initial speed of 80 ft/sec at an angle of 30° with the horizontal.a) Find parametric equations that give the position of the ball at time t, in
A projectile is launched from the ground with an initial speed of 200 ft/sec at an angle of 60° with the horizontal.a) Find parametric equations that give the position of the projectile at time t,
Graph.y = x3
Convert to radian measure.120°
Graph.x = y3
Convert to radian measure.-315°
Graph.f(x) = √x - 2
Convert to degree measure.π/3
Convert to degree measure.3π/4
Graph the plane curve described by x = cos3 t, y = sin3 t; 0 ≤ t ≤ 2π. Then find the equivalent rectangular equation.
Show that for any angle θ, the equation x2 + y2 = r2 becomes (x′)2 + (y′)2 = r2 when the rotation of axes formulas are applied.
Show that A + C = A + C.
Use a graphing calculator to find the vertex, the focus, and the directrix of each of the following.4.5x2 - 7.8x + 9.7y = 0
Use a graphing calculator to find the vertex, the focus, and the directrix of each of the following.134.1y2 + 43.4x - 316.6y - 122.4 = 0
For f(x) = (x - 3)2 + 4, find each of the following.f(2t)
For f(x) = (x - 3)2 + 4, find each of the following.f(t - 1)
Suppose that a comet travels in a parabolic orbit with the sun as its focus. Position a polar coordinate system with the pole at the sun and the axis of the orbit perpendicular to the polar axis.
For f(x) = (x - 3)2 + 4, find each of the following.f(t + 2)
Suppose that a comet travels in a parabolic orbit with the sun as its focus. Position a polar coordinate system with the pole at the sun and the axis of the orbit perpendicular to the polar axis.
Graph the plane curve given by the set of parametric equations and the restrictions for the parameter. Then find the equivalent rectangular equation.x = 2 cos t, y = 2 sin t; 0 ≤ t ≤ 2π
Hailey’s Frame Shop has been commissioned to frame 5 black-and-white photos for an island resort. Each photo has a perimeter of 68 in. and a diagonal of 26 in. Find the dimensions of the
Graph the plane curve given by the set of parametric equations and the restrictions for the parameter. Then find the equivalent rectangular equation.x = 3 sin t, y = cos t; 0 ≤ t ≤ 2π
Find two sets of parametric equations for the given rectangular equation.y = 2x - 3
Find two sets of parametric equations for the given rectangular equation.y = x2 + 4
projectile is launched from the ground with an initial speed of 150 ft/sec at an angle of 45° with the horizontal.a) Find parametric equations that give the position of the projectile at time t, in
Consider the graphs offor e = 0.2, 0.4, 0.6, and 0.8. Explain the effect of the value of e on the graph. r = e 1 - e sin 0
Which of the following cannot be a number of solutions possible for a system of equations representing an ellipse and a straight line?A. 0B. 1C. 2D. 4
Use a graphing calculator to graph each of the following on the given interval and approximate the zeros. f(x) cos x - X 1 ; [-12, 12]
Use a graphing calculator to graph each of the following on the given interval and approximate the zeros. f(x) = x³ sinx; [-5,5]
Use a graphing calculator to graph each of the following on the given interval and approximate the zeros. f(x) (sin x)² x [-4,4]
The temperature T of a patient during a 12-day illness is given bya) Graph the function on the interval [0, 12].b) What are the maximum and minimum temperatures during the illness? T(t) = 101.6° +
A satellite circles the earth in such a way that it is y miles from the equator (north or south, height not considered) t minutes after its launch, whereWhat are the amplitude, the period, and the
A company in a northern climate has sales of skis as given bywhere t is the time, in months (t = 0 corresponds to July 1), and S(t) is in thousands of dollars.a) Graph the function on a 12-month
An airplane flies 150 km from an airport in a direction of 120°. How far east of the airport is the plane then? How far south? gift W 270° 0° N 120⁰ E 90° 150 km S 180°
The cross-section of a water wave is given bywhere y is the vertical height of the water wave and x is the distance from the origin to the wave.What are the amplitude, the period, and the phase
An airplane leaves an airport and travels for 100 mi in a direction of 300°. How far north of the airport is the plane then? How far west? 100 mi W 270° 0° N 300° S 180° E 90°
Suppose that the motion of a spring is given by d(t) = 6e-0.8t cos (6πt) + 4, where d is the distance, in inches, of a weight from the point at which the spring is attached to a ceiling, after t
Graph the function. Sketch and label any vertical asymptotes. f(x) = 1 2 x². X - 25
Find the six trigonometric function values of α. 20 b
An airplane travels at 150 km/h for 2 hr in a direction of 138° from Omaha. At the end of this time, how far south of Omaha is the plane?
An airplane travels at 120 km/h for 2 hr in a direction of 319° from Chicago. At the end of this time, how far north of Chicago is the plane?
On March 31, 2014, the world’s tallest ferris wheel, the High Roller, opened in Las Vegas at the LINQ. Each cabin, which can fit up to 40 passengers, is 220 ft from the center of the wheel. The
Show that the area of this triangle is 1/2 ab sin θ. b a 0
Given that cos θ = 0.9651, find csc (90° - θ).
The valve cap on a bicycle wheel is 12.5 in. from the center of the wheel. From the position shown, the wheel starts to roll. After the wheel has turned 390°, how far above the ground is the valve
Graph the function. Sketch and label any vertical asymptotes.g(x) = x3 - 2x + 1
Given that sec β = 1.5304, find sin (90° - β).
Find the x-intercept(s) of the graph of the function.f(x) = 12 - x
Find the x-intercept(s) of the graph of the function.g(x) = x2 - x - 6
Find the exact acute angle θ for the given function value. cos 0 2
Find the reference angle and the exact function value if they exist.tan 330°
Find a positive angle and a negative angle that are coterminal with the given angle.-2π/3
Consider the coordinates on the unit circle for Exercises.In which quadrants is the sine function positive? negative?
Convert to D°M′S″ notation. Round to the nearest second.2.4°
Find the function value. Round to four decimal places.sec 240°55′
Find the function value. Round to four decimal places.csc 520°
Find the function value. Round to four decimal places.sin 3824°
Use a graphing calculator to graph each of the following on the given interval and approximate the zeros. f(x) sin x X [-12, 12]
Find the exact acute angle θ for the given function value. cot A احساس
Given thatsin 35° = 0.5736,cos 35° = 0.8192,tan 35° = 0.7002,find the trigonometric function values for 215°.
Find the acute angle θ, to the nearest tenth of a degree, for the given function value.sec θ = 1.279
Find the acute angle θ, to the nearest tenth of a degree, for the given function value.csc θ = 1.147
In Exercises, find the signs of the six trigonometric function values for the given angles.290°
Find the acute angle θ, to the nearest tenth of a degree, for the given function value.cos θ = 0.3842
Find the acute angle θ, to the nearest tenth of a degree, for the given function value.tan θ = 0.2226
Find the reference angle and the exact function value if they exist.cot ( -90°)

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