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Mathematics LibreTexts

8.11.2: Practice Test

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Practice Test

1.

Assume α is opposite side a,β is opposite side b, and γ is opposite side c. Solve the triangle, if possible, and round each answer to the nearest tenth, given 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) to polar coordinates, and then plot the point.

5.

Convert (2,π3) to rectangular coordinates.

6.

Convert the polar equation to a Cartesian equation: x2+y2=5y.

7.

Convert to rectangular form and graph: 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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