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Algebra and Trigonometry

Practice Test

Algebra and TrigonometryPractice Test

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.

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=3−5sinθ. r=3−5sinθ.

11.

Find the absolute value of the complex number 5−9i. 5−9i.

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 −5−i −5−i 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 u⋅v. u⋅v.

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.

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