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    Pre Cal Long Quiz 2

    Uploaded by

    Jincent Roble
    This document contains a number of problems involving converting between polar and rectangular coordinates, finding trigonometric functions given angle measures, solving trigonometric equations, identifying conic sections, and finding polar equations of conics. The problems cover a range of skills related to trigonometry and coordinate geometry.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    Pre Cal Long Quiz 2

    Uploaded by

    Jincent Roble
    38 views10 pages
    This document contains a number of problems involving converting between polar and rectangular coordinates, finding trigonometric functions given angle measures, solving trigonometric equations, identifying conic sections, and finding polar equations of conics. The problems cover a range of skills related to trigonometry and coordinate geometry.

    Original Title

    PRE-CAL-LONG-QUIZ-2

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    © © All Rights Reserved

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    This document contains a number of problems involving converting between polar and rectangular coordinates, finding trigonometric functions given angle measures, solving trigonometric equations, identifying conic sections, and finding polar equations of conics. The problems cover a range of skills related to trigonometry and coordinate geometry.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    38 views10 pages

    Pre Cal Long Quiz 2

    Uploaded by

    Jincent Roble
    This document contains a number of problems involving converting between polar and rectangular coordinates, finding trigonometric functions given angle measures, solving trigonometric equations, identifying conic sections, and finding polar equations of conics. The problems cover a range of skills related to trigonometry and coordinate geometry.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    You are on page 1of 10

    KAYA

    MO
    YAN!
    Identify the conic of 

    A: Parabola

    Convert the polar equation to rectangular form. 

    A:

    Convert the polar equation to rectangular form.

    A: X2 + 4y – 4 = 0

    Convert the rectangular equation to polar form. Assume a > 0.


    y=4
    A: R = 4 csc θ

    Convert the polar equation to rectangular form.

    A: (x2 + y2)2 = 6x2y – 2y3

    Plot the point given in polar coordinates and find two additional polar representations of the point,
    using -2π < θ < 2π. 

    (0,−7π60,−7π6)

    A:
    Write the expression as the sine, cosine, or tangent of an angle.
    sin 3 cos 1.2 - cos 3 sin 1.2
    sin 1.8
    Answer:

    Solve the equation for exact solutions over the interval [0, 2π]. 

    A:

    Find a polar equation of the conic with its focus at the pole.
    Conic: Hyperbola, Eccentricity: e = 2, Directrix: x = 1

    A:

    Convert the polar equation to rectangular form. 

    A:

    Find the exact value of the trigonometric function given that  sinu=513sinu=513 and
    cos .v=−35v=−35  (Both are in Quadrant II.) Note that answers in fractions must be
    entered like so: 4/5, 1/2, 3/4, -(5/10)
    sin (u + v)
    A: -(63/65)

    Give all exact solutions over the interval [00, 3600].


    sin2θ=2cos2θ
    A: 45° + 360°n, 90° + 360°n, 225° + 360°n, 270° + 360°n, where n is any integer

    Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as
    appropriate. 

    A:

    A point in polar coordinates is given. Convert the point to rectangular coordinates.


    A: (0, 3)

    Convert the rectangular equation to polar form. Assume a > 0. 


    y2 - 8x - 16 = 0

    A:

    Find the exact value of the trigonometric function given that and
    (Both u and v are in Quadrant III.) Note that answers in fractions must be entered like so: 4/5, 1/2,
    3/4, -(5/10)
    cos (u + v)
    A: 3/5

    Give all exact solutions over the interval [00, 3600].

    A: 0° + 360°n, 30° + 360°n,150° + 360°n, 180° + 360°n, where n is any integer

    Solve each equation for exact solutions over the interval [0 0, 3600]. 
    (tanθ−1)(cosθ−1)=0
    A: {00, 450, 2250}

    Convert the polar equation to rectangular form. 


    r=4

    A:

    Convert the polar equation to rectangular form.


    A: X2 + 4y – 4 = 0

    Identify the conic of 


    A: ellipse

    Solve the equation for exact solutions over the interval [0, 2π]. 

    A:

    Give all exact solutions over the interval [00, 3600].


    csc2θ2=2secθ
    A: 60° + 360°n, 300° + 360°n, where n is any integer.

    Find a polar equation of the conic with its focus at the pole.
    Conic: Parabola, Vertex or vertices: (1, -π/2)

    A:

    Convert the rectangular equation to polar form. Assume a > 0. 


    X2 + y2 = a2

    A:

    Find a polar equation of the conic with its focus at the pole.
    Conic: Ellipse, Vertex or vertices: (2, 0), (10, π)

    A:

    Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as
    appropriate. 

    A:
    Convert the rectangular equation to polar form. Assume a > 0. 
    3x - y + 2 = 0

    A:

    Convert the polar equation to rectangular form.

    A: y = 4

    Solve the equation for exact solutions over the interval [0, 2π]. 

    A:

    Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as
    appropriate. 

    A:

    Convert the polar equation to rectangular form.

    A: X2 + y2 – x2/3 = 0

    Convert the rectangular equation to polar form. Assume a > 0. 


    x2 + y2 - 2ax = 0

    A:

    Find a polar equation of the conic with its focus at the pole.
    Conic: Parabola, Eccentricity: e = 1, Directrix: x = -1

    A:
    Find the exact value of each expression.
    a. cos (120° + 45°)                            b. cos120° + cos45°

    A:

    Solve the equation for exact solutions over the interval [0, 2π]. 

    A:

    Convert the polar equation to rectangular form.

    A: 4x2 – 5y2 – 36y – 36 = 0

    Identify the conic of 


    A: parabola

    Convert the polar equation to rectangular form. 

    A:

    Convert the rectangular equation to polar form. Assume a > 0. 


    Xy = 16
    A:

    Write the expression as the sine, cosine, or tangent of an angle. 

    A: tan 3x
    Solve each equation for exact solutions over the interval [0 0, 3600]. 

    A: {300, 2100, 2400, 3000}

    Convert the rectangular equation to polar form. Assume a > 0.


    x = 10
    R = 10 sec θ

    Find the exact value of the cosine of the angle by using a sum or difference formula. 
    195° = 225° - 30°

    A:

    Solve the equation for exact solutions over the interval [0, 2π]. 
    tan 4x = 0

    A:

    Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as
    appropriate. 

    A: .9 + 2nπ, 2.3 + 2nπ, 3.6 + 2nπ, 5.8 + 2nπ, where n is any integer

    Solve each equation for exact solutions over the interval [0 0, 3600]. 

    A:  {900, 2100, 3300}

    Solve the equation for exact solutions over the interval [0, 2π]. 

    A:
    Plot the point given in polar coordinates and find two additional polar representations of the point,
    using -2π < θ < 2π. 

    A:

    Convert the rectangular equation to polar form. Assume a > 0.


    x2 + y2 = 9 
    A: R = 3

    Plot the point given in polar coordinates and find two additional polar representations of the point,
    using -2π < θ < 2π. 

    A:

    Plot the point given in polar coordinates and find two additional polar representations of the point,
    using -2π < θ < 2π. 
    A:

    Find a polar equation of the conic with its focus at the pole.
    Conic: Parabola, Vertex or vertices: (5, π)

    A:

    A point in polar coordinates is given. Convert the point to rectangular coordinates.

    A:

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