precalc problems?

1.Fina states that the equation 2sin(3x)=1 and 2cos(3x)=1 have the same solutions. Is Fina’s claim true or false? Justify your reasoning by showing some of the solutions to each equation

2.A teacher told her students to plot the coordinate pair ( 3, 3π/4)

Jessie plotted this point using Cartesian graph paper. James, her table partner, decided to plot this point using polar graph paper. Did Jessie or James use the correct graph paper? Explain your reasoning.

2 Answers

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  • 2 years ago
    Favorite Answer

    (1) Fina is false . For

    2sin(3x)=1

    =>

    sin(3x)=1/2

    =>

    3x=kpi+[(-1)^k](pi/6)----(1)

    2cos(3x)=1

    =>

    cos(3x)=1/2

    =>

    3x=2kpi+/-(pi/3)--------(2)

    (1)=(2)

    =>

    kpi+[(-1)^k](pi/6)=2kpi+/-(pi/3)

    =>

    kpi=[(-1)^k](pi/6)-/+(pi/3)

    =>

    k={[(-1)^k]-/+2} /6

    The result is impossible for

    the LHS is an integer while the

    RHS is a fraction=> no integral k

    exists such hat (1)=(2) or say,

    2sin(3x)=1 & 2cos(3x)=1 have

    same solution.

    (2)

    Jame uses the correct graph paper.

    If the teacher has told them to plot the points

    for a circle, not just one point. Jessie would

    have plotted out a straight line, while Jame

    plotted out a true circle.

  • 2 years ago

    #1. False. For example, x = 10 degrees is a solution of the first equation but not of the second equation.

    #2. Probably the (3, 3pi/4) was a polar specification rather than a Cartesian specification...there IS such a point as (3, 3pi/4) in the Cartesian plane, but the "3pi/4" is more suggestive of the radian measure of an angle, than of a linear measurement.

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