Additional Topics in Trigonometry
Review Problems

1.  Plot the point corresponding to z = \/3 - i in the complex plane, and write an expression for z
     in polar (trigonometric) form.

2.  Write 2(cos 30^o + i sin 30^o) in rectangular (standard) form.

3.  Let z = 3(cos 20^o + i sin 20^o) and w = 5(cos 100^o + i sin 100^o).  Find
     a.  zw
     b.  z/w

4. Write [2(cis 20^o)]³ in standard form.

5. Write (1 + i)⁵ in standard form.

6.  Find the complex cube roots of -1 + \/3 i.

7.  Find the component vector of the vector whose initial point is (-1,2) and whose terminal point 
     is (4,6).

8.  If v = 2i + 3j and w = 3i - 4j, find
     a.  v + w
     b.  v - w
     c.  3v
     d.  2v - 3w
     e.  ||v||
     f.  v×w 

9. Find a unit vector in the same direction as v = 4i - 3j.

10.  An airplane maintains a constant airspeed of 500 mph in the direction due south.  The
       velocity of the jet stream is 80 mph in a north-easterly direction.  Find the actual speed of the
       aircraft relative to the ground and find the bearing of the actual line of travel.

11.  Find the angle between u = 4i - 3j  and  v = 2i + 5j.

12.  Are the vectors v = 3i - j and w = 6i - 2j parallel, orthogonal, or neither?

13.  Are the vectors v = 2i - j and w = 3i + 6j parallel, orthogonal, or neither?

14.  A girl is pulling a wagon with a force of 50 lbs (travels through the handle).  How much work
       is done in moving the wagon 100 feet if the handle makes an angle of 30^o with the ground?

15.  A truck with a gross weight of 36000 pounds is parked on a 12^o slope.  Find the force 
       required to keep the truck from rolling down the hill.

16.  Solve:  x⁵ - 32 = 0

17.  Find  ln (-3.49).

18.  Write  -3\/2 /2  +  3\/2 /2  i  in exponential form.
 

Go to Precalculus Page
Go to Precalculus Lesson Page
Go to Additional Topics in Trigonometry