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8.11.2: Practice Test

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    116149
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    Practice Test

    1.

    Assume α α is opposite side a,β a,β is opposite side b, b, and γ γ is opposite side c. c. Solve the triangle, if possible, and round each answer to the nearest tenth, given β=68°,b=21,c=16. β=68°,b=21,c=16.

    2.

    Find the area of the triangle in Figure 1. Round each answer to the nearest tenth.

    A triangle. One angle is 60 degrees with opposite side 6.25. The other two sides are 5 and 7.
    Figure 1
    3.

    A pilot flies in a straight path for 2 hours. He then makes a course correction, heading 15° to the right of his original course, and flies 1 hour in the new direction. If he maintains a constant speed of 575 miles per hour, how far is he from his starting position?

    4.

    Convert ( 2,2 ) ( 2,2 ) to polar coordinates, and then plot the point.

    5.

    Convert ( 2, π 3 ) ( 2, π 3 ) to rectangular coordinates.

    6.

    Convert the polar equation to a Cartesian equation: x 2 + y 2 =5y. x 2 + y 2 =5y.

    7.

    Convert to rectangular form and graph: r=3cscθ. r=3cscθ.

    8.

    Test the equation for symmetry: r=4sin( 2θ ). r=4sin( 2θ ).

    9.

    Graph r=3+3cosθ. r=3+3cosθ.

    10.

    Graph r=35sinθ. r=35sinθ.

    11.

    Find the absolute value of the complex number 59i. 59i.

    12.

    Write the complex number in polar form: 4+i. 4+i.

    13.

    Convert the complex number from polar to rectangular form: z=5cis( 2π 3 ). z=5cis( 2π 3 ).

    Given z 1 =8cis( 36° ) z 1 =8cis( 36° ) and z 2 =2cis( 15° ), z 2 =2cis( 15° ), evaluate each expression.

    14.

    z 1 z 2 z 1 z 2

    15.

    z 1 z 2 z 1 z 2

    16.

    ( z 2 ) 3 ( z 2 ) 3

    17.

    z 1 z 1

    18.

    Plot the complex number −5i −5i in the complex plane.

    19.

    Eliminate the parameter t t to rewrite the following parametric equations as a Cartesian equation: { x(t)=t+1 y(t)=2 t 2 . { x(t)=t+1 y(t)=2 t 2 .

    20.

    Parameterize (write a parametric equation for) the following Cartesian equation by using x( t )=acost x( t )=acost and y(t)=bsint: y(t)=bsint: x 2 36 + y 2 100 =1. x 2 36 + y 2 100 =1.

    21.

    Graph the set of parametric equations and find the Cartesian equation: { x(t)=2sint y(t)=5cost . { x(t)=2sint y(t)=5cost .

    22.

    A ball is launched with an initial velocity of 95 feet per second at an angle of 52° to the horizontal. The ball is released at a height of 3.5 feet above the ground.

    1. Find the parametric equations to model the path of the ball.
    2. Where is the ball after 2 seconds?
    3. How long is the ball in the air?

    For the following exercises, use the vectors u = i − 3j and v = 2i + 3j.

    23.

    Find 2u − 3v.

    24.

    Calculate uv. uv.

    25.

    Find a unit vector in the same direction as v. v.

    26.

    Given vector v v has an initial point P 1 =( 2,2 ) P 1 =( 2,2 ) and terminal point P 2 =( 1,0 ), P 2 =( 1,0 ), write the vector v v in terms of i i and j. j. On the graph, draw v, v, and v. v.


    8.11.2: Practice Test is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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