1. In ABC, C is a right angle and BC= 11. If the measure of angle B= 30degrees, find AC. A) (11sqrt3)/3
B) 3sqrt/11
C)11/2
D)11sqrt3/2

2.which of the following angles has a reference angle of pi/8?
A)-51pi/8
B)11pi/8
C)-33pi/8
D)27pi/8

3.Your town’s public library is building a new wheelchair ramp to its entrance. By law, the maximum angle of incline for the ramp is 4.76 degrees. The ramp will have a vertical ride of 2.5 ft. What is the shortest horizontal distance that the ramp can span?
A)11.9ft
B)30.0ft
C)4.3ft
D)19.1ft

4. find the exact value of sec theta if cot theta= -1/2 and the terminal side of theta lies in quadrant II.
A)sec theta= -sqrt5/2
B)sec theta= sqrt5/2
C)sec theta=-sqrt5
D)sec theta=sqrt5

5.which of the following has the same value as sin(2pi/3)? Select all that apply.
A)cos(pi/6)
B)cos(pi/3)
C)sin(5pi/3)
D)cos(7pi/6)
E)cos(11pi/6)

6.Which trigonometric function is equivalent to f(x)=sin x?
A) f(x)=cos(-x+(3pi/2))
B) f(x)=cos(x+(pi/2))
C) f(x)=cos(-x+(pi/2))
D) f(x)=cos(-x+pi)

7.which trigonometric function requires a domain restriction of [(-pi/2),(pi/2)] to make it invertible?
A) f(x)=sin x
B) f(x)=cos x
C) f(x)=tan x
D) f(x)=csc x
E) f(x)=sec x
F) f(x)=cot x

8.what is the horizontal shift of the function y= 3sin(4x-pi)?
A)pi units to the right
B)pi/2 units to the right
C)pi/3 units to the left
D)pi/4 units to the right

9.which is the exact value of cos (-75 degrees)?
A) (sqrt6 +sqrt2)/4
B)(sqrt6 -sqrt2)/4
C) (-sqrt6 +sqrt2)/4
D)-(sqrt6 +sqrt2)/4

10.The sides of a triangle are 17 ft, 19ft, and 15ft. Find the measure of the angle opposite the longest side. Round your answer to the nearest degree.
A)107
B)73
C)59
D)49

11.find all solutions of the equation 2sin 2x cosx -sin2x=0 over the interval -pi/2 A)x=-pi/6, 0, pi/6, pi/2
B)x=-pi/3, -pi/4, pi/4, pi/3
C)x=-pi/4, -pi/6, pi/6, pi/4
D)x=-pi/3, 0, pi/3, pi/2

12. Which polar coordinates represent the same point as the rectangular coordinate (1,-2)? Select all that apply
A)(sqrt5, 63.4 degrees)
B)(sqrt5,296.6 degrees)
C)(-sqrt5, 116.6 degrees)
D)(-sqrt5, 153.4 degrees)

13. Which polar equation represents an ellipse?
A)r=3/(2-5sin theta)
B) r=2/(2-sin theta)
C) r=4/(3+3 cos theta)
D) r=5/(3+4 cos theta)

14. Use DeMoivre’s Theorem to find (2cis pi/9)^3.
A)4+4 sqrt3i
B)3+3 sqrt3i
C)4sqrt3 +4i
D)3sqrt3 +3i

15.which of the following points could be the initial point of vector v if it has a magnitude of 10 and the terminal point (-2,4)?
A)(-.2,.4)
B)(-8,-4)
C)(-12, -6)
D)(1,3)

16. Given vectors u=(-6,4) and v=(7,10), determine if the vectors are orthogonal. If they are not orthogonal, find the angle between them.
A)the vectors are not orthogonal
B)the vectors are not orthogonal. The angle between the two vectors is 91.3
C) the vectors are not orthogonal. The angle between the two vectors is 98
D) the vectors are not orthogonal. The angle between the two vectors is 80.6

17.which statement matches the vector operation shown on the coordinate grid?
A)v+w=u for v=5i+4j, w=2i-3j, and u=3i+7j
B) v+w=u for v=5i+4j, w=2i-3j, and u=7i+j
C) v+w=u for v=5i+4j, u=7i+j, and w=12i+5j
D) v+w=u for v=5i+4j, u=7i+j, and w=2i-3j

18. Two forces act on an object. The first force has a magnitude of 360 Newton’s and acts at an angle of 30degrees as measured from he horizontal. The second force has a magnitude of 240 newtons and acts at an angle of 135 degrees as measured from the horizontal. Determine the vector v that represents the resultant force.
A)v=(180 sqrt3 +120 sqrt2)i +(180+120 sqrt2)j
B) v=(180 sqrt3 -120 sqrt2)i +(180+120 sqrt2)j
C) v=(180 +120 sqrt2)i +(180+ sqrt3 +120 sqrt2)j
D) v=(180 -120 sqrt2)i +(180+ sqrt3 +120 sqrt2)j

19. For v= -3i+9j, find the unit vector u in the direction of v.
A) u= -(sqrt2/4)i +(3sqrt2/4)j
B)u= -(sqrt10/10)i + (3sqrt10/10)j
C)u=-1/4i +3/4j
D)u=-i+j

20. Which of the following is a point on the plane curve defined by the parametric equations?
X=3t
Y=18t^2 +12t+2
A)(-1,0)
B)(-3,-28)
C)(-1,8)
D)(-3,128)

21. Write the following parametric equations as a polar equation.
X=2t
Y=t^2
A)r=4 cot theta csc theta
B) r=4 tan theta sec theta
C) r=2 cot theta csc theta
D) r=2 tan theta sec theta

22. A baseball player hits a ball at an angle of 56 degrees and at a height of 4.2 ft. If the ball’s initial velocity after being hit is 154 ft/sec and if no one catches the ball, when will it hit the ground? Remember that the acceleration due to gravity is 32 ft/s^2
A)8.01 seconds
B)7.98 seconds
C)5.43 seconds
D)5.38 seconds

23. Which set of parametric equations represents the function y=2x^2 -18x+35?
A)x=t-3, y=2t^2 -30t +105
B)x=2t, y=t^2 -9t+35
C)x=t +5, y=2t^2 +2t +5
D)x=t+3, y=2t^2 -6t -1

24. Which is a polar form of the following parametric equations?
X=4sin^2 theta
Y=4sin theta cos theta
A) r= 1/4 sin theta cos theta
B) r=2
C) r=16sin^2 theta
D)r=4 sin theta

25. Find lim (x—>2) for (x^2 +3x -10) / (x-2)
A)0
B)1
C)5
D)7