Download final exam review sheet

Name ____________________________________, Period _____ ,
Date ____________
FINAL EXAM REVIEW SHEET – 1ST SEMESTER TRIG
The following problems are representative samples of what you can expect on the final.
Show work and be neat. Put all final answers in a box. Each correct answer = 5 points.
1. If sec  
25
and sin  < 0, calculate tan  .
7
2. Prove the following identity. Show each step neatly and clearly!
sin x  cos x sin x

sec x  csc x sec x
3. Evaluate the following inverse trig expression:


 2
  sin 1  1
sec cos 1



 2 
4. Use the given information to express sin 2 in terms of 
x +1 = 3sin 


   
2

5. Calculate the exact value of cos(15o) without a calculator.
6. Determine an equation for the trig function represented by the graph.
Use the formula: y = Acos(Bx + C) + D or y = Asin(Bx + C) + D)
A= ___________
B = ___________
C = ___________
D = ___________
One possible equation is: ____________________________
7. Solve the following trig equation. Identify the primary and general solutions.
2cos2x - sinx - 1 = 0
Primary Solutions are: ___________________________
General Solutions are : __________________________
8. A building contractor wants to put a fence around the perimeter of a flat lot that has the shape of a right
triangle. One angle of the triangle is 41.4o, and the length of the hypotenuse is 58.5 feet. Find the length of
fencing required. Round the answer to one decimal place.
9. After the hurricane, the small tree in my neighbor’s yard was leaning. To
keep it from falling, we nailed a 6-foot strap into the ground 4 feet from the
base of the tree. We attached the strap to the tree 3½ feet above the
ground. How far from vertical was the tree leaning (i.e. calculate the angle  ).
Round your answer to the nearest tenth of a degree.
10. Calculate the area of the shaded region shown in the picture.
Give the exact answer only.
11. Given three vectors a = 2,3 , b = 5,4 , c=  2,0
Compute the following quantity:
1
3b  4a 
3b  4c
12. Compute the horizontal and vertical components (Vx and Vy) of the following velocity vector.
V = 35 m/s and  = 60o. The initial point for vector is the origin. The angle  denotes the angle
(measured counterclockwise) from the x-axis to the vector. Make a sketch to help you.
Vx = __________ , Vy ____________
13. Given the vectors: A = 3i – 2j , B = 6j, and C = -5i + 3j.
Calculate the following dot-product quantity:
A  ( B + C)
14. Given the parametric equations x = 4sint , y = 2cost .
a. Calculate the exact position coordinate (x,y) for t =

sec
3
b. Make a sketch of the curve by calculating and plotting the (x ,y)
position coordinates for the following values of t: t = 0,
3
, 2
2

, ,
2
c. Convert the two equations into to a single rectangular equation.
d. Describe the shape and direction of the curve in a few sentences below.
3 ) to polar form (r,  )
15. Convert the rectangular coordinates (x , y) = (3,
16. Convert the polar coordinates (r,  ) =
(-5 ,

) to rectangular form (x , y)
4
17. Convert the following polar equation to rectangular form: r 2 
1
3  3 cos 2 
18. Convert the following rectangular equation to polar form: 2x – 3y = 5
19. Determine the polar coordinates A, B, C, and D on the
4-leaf petal graph shown:
A = ___________ , C = ____________
B=____________ , D = ____________
20. You are given the following polar equation: r = 1 – sin 
a. Check for x -axis or y-axis symmetry below.
x-axis: Test1
y-axis: Test 2
y-axis: Test 3
b. Explain in a few sentences why it is beneficial to check for symmetry.
c. Graph of the equation on the attached polar grid. Use the following table of values to
generate your points. Then make the graph in 2 sections – using symmetry to help!

0
r

6

4

3

2
Sketch
Section
#1

7
6
5
4
4
3
3
2
Sketch
Section
#2
BONUS PROBLEM:
A laser beam is to be directed through a small hole in the center of a circle of radius 10 feet. The origin of the
beam is 35 feet from the circle (see the picture). At what angle of elevation should the beam be aimed to
ensure that it goes through the hole?