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)

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

Y= 2cos (x/2 –

- find the angle between 0 and 2that is coterminal with each angle given
- 17 b – (15
- In a RIGHT triangle ABC, <C is a right angle. BC=6 AB=10 Find sec A and csc A
- 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)

- 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.

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

* *

**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

- Solve the equation in the interval [0, 2π)

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

- Solve the equation in the interval [0,2π)

Sin x= cos 2x

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

20.

- 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
- Find and given that u=2i – j and v =i
- Find the value of sec ()) no calculator values

I really enjoyed teaching you!

Have wonderful days ahead!

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