MATH D FINALS    150 POINTS                                                                    July 29 2021

Please show work neatly and completely with formulas.

Use calculators only for unknown angles

Points.  All questions 7 points each except #7 (8 points) and #20 (10 points)

  1. The point P(x, y) is on the unit circle in quad 2 .If x=-/6 find y
  2. Find the exact value of sin (19  and cos (5)
  3. If the terminal points determined by (, -) find Sint, cost and tant
  4. Find the exact value of sin (30∘) ^2 – (cos30∘) ^2
  5. Find the value of sin θ and tan θ if the point (-3,4) is on the terminal side of
  6. Find the amplitude, period and phase shift of the function (no graphs)

Y= 2cos (x/2 –

  1. find the angle between 0 and 2that is coterminal with each angle given
  2. 17 b   – (15
  3. In a RIGHT triangle ABC, <C is a right angle.  BC=6     AB=10    Find sec A and csc A
  4. From the top of a 250 ft high light house, the angle of depression to a ship in the ocean is 18∘. How far is the ship from the base of the light house?

. Find all angles between 0 and180∘ satisfying the given equation  (calculators)

  1. sin x =0.7

11 cot y = – 1.6

12.Find as fractions (no calculator values) of all trig functions if sin t = -1/2  and cos t  is positive

. Problems 13 and 14   refer to triangle ABC which is not necessarily a right triangle.

  1. 13. If A = 34° and B = 76°, and a = 4.3 inches, use the law of sines to find b


  1. 14. If C = 75°, a = 12 centimeters, and b = 15 centimeters, use the law of cosines to find c.

15.Use Heron’s formula to find the area of the triangle with the sides 10,12,20 units

  1. Solve the equation in the interval [0, 2π)

(cscx)^2 -4 = 0 (no calculators for any of the problems for known angles)

  1. Solve the equation in the interval [0,2π)

Sin x= cos 2x

  1. Find exact value (no calculators) cos(5π/12)
  2. simplify     cos 75∘ cos 30∘+ sin75∘sin30∘


  1. Let u be a vector with initial point P (5,1) and terminal point Q (2,2). Express u in terms of i and j
  2. Find and given that u=2i – j and v =i
  3. Find the value of sec ()) no calculator values



I really enjoyed teaching you!

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