Transcript Sample Final

SAMPLE
Final
(200 points Total)
Math 240
Professor O. LePoint
Instructions: Answer the following questions without notes or the book. You can use
calculators. Complete as many questions within 2 hours. Partial credit can be given for
each section.
Question 1: Give the definition for the following in the space provided below:
•
Vertical Asymptotes of y = tan x
•
Supplementary Angles
•
Reference Angle
•
SOH CAH TOA
•
Inverse Function
Name________________
Student ID____________
Question 2: Convert 18° to π radians and find 2 coterminal angles in
radians. Show all work.
Question 3: The following two triangles are similar. Find x and y.
Hint: Draw the triangles separately. Your answers will be in
variables.
X -2y
10
74°
X-5
X +y
20
74°
Question 4: Solve sin2 θ + 3sin θ + 2 = 0.
Question 5:
Give all the solutions for θ.
Solve 2 sin x + (sin2 x + cos2 x ) = 0
Question 6: What is the sine, cosine, and tangent values of θ in standard
position if the terminal side of θ is defined by x+2y =0, for x≥ 0.
Box your answers. (15 points)
Name________________
Student ID____________
Question 7:
Give the fractions for the following trigonometric functions using the
figure. Give the restrictions.
If θ = tan -1 u
θ
•
Sin θ = __________________________________
•
cos θ = __________________________________
•
cot θ = __________________________________
Question 8 : Give the exact value of the expression without using a calculator
cos ( tan -1 5/12 - tan -1 3/4 ).
Question 9:
Write sin 2θ – sin 4θ as a product of two functions.
Name________________
Student ID____________
Question 10:
Use the half angle identity to find cos (-22.5°).
Question 11:
Show
[ HINT: start with the left side, and multiply top and
bottom by the same expression.) Remember to FOIL. ]
1  sin x
cos x

cos x
1  sin x
Question 12 : Graphing y = 2 sin (2x) + 1
•
What is the period of y = 2 sin (2x) + 1 ?
•
Evaluate y = 2 sin (2x) + 1 , on an interval starting with 0 and ending with
π.
•
Sketch y = 2 sin (2x) + 1 in the space provided below
3
2
1


2
0

4
3
4
3
4

Name________________
Student ID____________
CONTINUED
Question 13 :
•
After seeing the lectures, what basic math topic, which
was once very confusing, is easier to understand now?
•
What teaching methods helped you understand the
difficult concepts better?
•
What were your original expectations of Trigonometry?
•
Do you plan to take more math classes? If so, what
classes?
•
What surprises did you encounter in this class?
Name________________
Student ID____________
CONTINUED
Question 14:
The Hubble telescope traveling in a circular orbit 1600 km above the surface of
the Earth takes 2 hours to make an orbit. The radius of earth is 6400 km.
1600
6400
•
Find the linear speed of the telescope. Show all work and equations.
•
Find the distance the telescope travels in 4.5 hours. Show all work and equations.
Question 15:
Graph
y= sin x
Y=arccos x on the same graph
Name________________
Student ID____________
CONTINUED
Question 15: Prove the following
Question 16: Prove the following
Question 17: Perform the Following