1120 Trigonometry Final Exam Fall 1998



1. Given triangle ABC where angle ABC is a right angle with sides AB = 4 inches and BC = 6 inches , find the exact values of the following:

  1. sin A =
  2. cot A =
  3. sec A =

2. Knowing -1 < sin (x) < 1, find two functions g and f that bound sin (x ) + 2 + 2x.

g ( x) < sin (x) + 2 + 2 x < h (x)

  1. g( x) =
  2. h( x) =

3. Given f(x) = 2 cos (x - Pi) + 1, find the following:

domain: range:
period: phase shift:
amplitude: vertical shift :






4. Given 3 sec 3x, find the following:

domain: range:
period: phase shift:
vertical shift : zeros :

5. The horizontal distance of a thrown ball is given by d = (1/32) vo 2 sin (2A), where A is the angle with the horizontal of the thrown object and vo is the initial velocity. If football was thrown a distance of 192 feet with an initial velocity of 64 feet per second, what is the angle that the ball was thrown?



6. A force of 4 units acts on a object at an angle of 30 o. A second force of 20 units acts on the same object at an angle of 90 o.

  1. Write the resultant force in rectangular format.
  2. Find the magnitude of this vector

7. Given the two vectors u = < -1,2> and v = <4, 8>

  1. Change u to a unit vector.
  2. 2 u + v =

8. Given triangle ABC where a = 8 inches , A = 36 o and B = 48 o, find the length of b. (Just set up the equation )

b =


9. Given z 1 = 3 + 6 i and z 2 = 4 + 5 i , find

  1. z 1 + z 2 =
  2. z 1 z 2 =
  3. Let z 1 = 3(cos 45 o + i sin 45 o) and z 2 = 2 ( cos 30 o + sin 30 o )
    1. Put your answer in the form a + bi.
    2. Find z 1/ z 2 =
    3. z 1 z 2 =

10 . Use De Moivre's Theorem to evaluate: Please simplify your answer.

[ 3 (cos Pi / 4 + i sin Pi / 4 )] 2 =



11. Find the parametric equation for the circle centered at ( -2,-1) and radius 4.

  1. x (t ) =
  2. y ( t ) =

12. Vertical projectile motion is given by y (t) = - 16 t 2 + ( v o sin0 ) t + y o. A ball is hit when it is 3 feet above the ground with an initial velocity of 120 feet per second. The ball leaves the bat at a 30 o angle with the horizon. Write parametric equations to describe the path of the ball.

  1. x ( t) =
  2. y ( t) =

13. Conics have the form Ax 2+ B x y + Cy 2 + Dx + Ey + F= 0 Using the discriminant, identify whether the conics below are parabolas, ellipses, or hyperbolas.

  1. 2 x 2 + 3 x y + 2 y 2 + .5 x + 3.1 y - 3 = 0
  2. x 2+ 4 xy + 4y 2 - 30 x - 90 y + 450 = 0
  3. x 2 - 3 x y + y 2 - 5 = 0
  4. Given the conic, x 2 - 3 x y + y 2 - 5 = 0 find the angle of rotation that eliminates the x y term.

14. Given an ellipse centered at ( 0, 0) with foci (-4, 0) and ( 4, 0) and a minor axis of length 6, find:

  1. the equation of the ellipse in standard form.
  2. Write the equation for the ellipse in parametric form.
    1. x (t) =
    2. y (t) =

15. Given the hyperbola find the following:

  1. center
  2. a =
  3. b =
  4. slope of the asymptotes =

16. Write the equation for a parabola with directrix y = -2, and focus (0, 2).



17. Convert 3 x + 4 y = 2 to the polar form.

18. Convert r sec0 = 3 to rectangular form.

UNIVERSITY OF COLORADO AT DENVER: MATH 1120: FALL 1998