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Algebra and Trigonometry

Practice Test

Algebra and TrigonometryPractice Test

Practice Test


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.


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

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?


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


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


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


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


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


Graph r=3+3cosθ. r=3+3cosθ.


Graph r=35sinθ. r=35sinθ.


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


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


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.


z 1 z 2 z 1 z 2


z 1 z 2 z 1 z 2


( z 2 ) 3 ( z 2 ) 3


z 1 z 1


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


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 .


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.


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


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.


Find 2u − 3v.


Calculate uv. uv.


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


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.

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