6.2
9.2
6.4
Name:______________________________________ Week #14/15
Trigonometry Diagnostic Test to prep for Final Exam Review Sheet
Score:___
90
Define Quadrant:_______________________________________________________________________
Define terminal ray:_____________________________________________________________________
1a. In what quadrant does the terminal ray of the angle
3π
4
lie? Draw it:
1b. In what quadrant does the terminal ray of the angle
π
6
lie? Draw it:
1c. In what quadrant does the terminal ray of the angle
−π
4
lie? Draw it:
1d. In what quadrant does the terminal ray of the angle
11π
4
lie? Draw it:
What are the Sum & Difference Formulas?
When do you use the Sum & Difference Formulas?
2a. Simplify the expression sin (34 ⁰ ) cos (56 ⁰ ) – cos (34 ⁰ )sin(56 ⁰ ).
2b. Simplify the expression sin (33 ⁰ ) sin(51 ⁰ ) – cos (33 ⁰ )cos(51 ⁰ ).
_______________________________
_______________________________
2c. Simplify the expression tan(30 ⁰ ) + tan(56 ⁰ )
1 – tan(30⁰)tan(56⁰)
2c. Simplify the expression sin (34 ⁰ ) sin(56 ⁰ ) + cos (34 ⁰ )cos(56 ⁰ ).
_______________________________
_______________________________
2e. Simplify the expression cos (
2π
3
) cos(
4π
3
) – sin (
2π
3
)sin(
4π
3
). _______________________________
3. On a 45⁰-45⁰-90⁰ triangle, a leg has the length 6. Draw the triangle and fill in all the angles and sides of the triangle.
4. On a 30⁰-60⁰-90⁰ triangle, the short leg has the length 6. Draw the triangle and fill in all the angles and sides of the triangle.

8.2
6.5
9.3
6.1
5. Find the exact values of the six trigonometric functions of the angle θ shown in the figure.
4
9
6a. The expression
can also be written as what other expression? (Hint: use formula page)
6b. The expression
2
2
can also be written as what other expression?
(Hint: use formula page)
6c. The expression
2
can also be written as what other expression? (Hint: use formula page)
6d. The expression
can also be written as what other expression? (Hint: use formula page)
2
7a. What is the exact value of sin -1 ( −
1
2
)?
7c. What is the exact value of cos -1 ( −
1
2
)?
7e. What is the exact value of arcsin ( −
1
2
)?
8a. Simplify: sin θ tan θ
7b. What is the exact value of sin -1 ( −
√3
2
)?
7d. What is the exact value of arctan ( −1 )?
8b. Simplify: cos θ csc θ
8c. Simplify: sin θ cos θ csc θ 8d. Simplify: cot θ tan θ

9.2
6.3
8.1
8.2
9a. What is the correct value of cot(arcsin(
4
5
)?
9a. What is the correct value of tan(arcsin(
3
5
)?
9a. What is the correct value of cot(arccos(
4
5
)?
9a. What is the correct value of cot(arctan(
12
)?
5
Define coterminal:____________________________________________________________________
Define supplementary:_________________________________________________________________
Define linear pair:_____________________________________________________________________
10a. Name a coterminal angle for 47⁰.
10b. Name a coterminal angle for 617⁰.
10c. Name a coterminal angle for -247⁰.
10d. Name a coterminal angle for 317⁰.
What are the Difference of Angles Formulas? (see #2)
11a. What is the exact value (no decimals) of sin 75⁰?
11b. What is the exact value (no decimals) of cos 75⁰?
11c. What is the exact value (no decimals) of tan 75⁰?
12a. Solve this equation for x: cos(6x) = −
1
2
Why are there more than one answers?
12b. Solve this equation for x: cos(2x) = −
1
2
Why are there more than one answers?
12c. Solve this equation for x: sin(6x) =
1
2
Why are there more than one answers?
12d. Solve this equation for x: cos(6x) = −
√3
2
Why are there more than one answers?

7.2
7.3
7.4
6.4
8.1
8.3
Page
449
Define reference angle:__________________________________________________________________
13a. What is the reference angle for 13 π ?
8
13b. What is the reference angle for 7 π ?
8
13c. What is the reference angle for 13 π ?
4
13d. What is the reference angle for --11 π ?
3
14a. Solve 2 cos x -- √3 = 0 over the interval 0 ≤ x< 2 π.
14b. Solve √2 tan x --1 = 0 over the interval 0 ≤ x< 2 π.
14c. Solve 2 sin x -- √3 = 0 over the interval 0 ≤ x< 2 π.
14d. Solve 4 tan x -- 2 = 0 over the interval 0 ≤ x< 2 π.
15a. What is the amplitude, period, and vertical slide of the sine function given in this picture:
Amplitude=___ period= ____ vertical slide=_________
15b. Graph 3 sin (2x- π ) +1. 15c. Graph -2 cos (x- π ) -1.
16b. The terminal ray of the angle β = −
16a. The terminal ray of the angle β =
2π
3
passes thru what point on the unit circle?
π
4
passes thru what point on the unit circle?
16c. The terminal ray of the angle β = −
π
6
passes thru what point on the unit circle?

6.1
6.2
6.3
6.4
10.1
10.2
6.4
6.3
6.3
17a. Convert 150⁰ to radian measure.
17b. Convert 290⁰ to radian measure.
17c. Convert -30⁰ to radian measure.
17d. Convert -170⁰ to radian measure.
17e. Convert 150⁰ to radian measure.
18a. Convert
π
5 to degree measure.
18b. Convert
2π
3 to degree measure.
18c. Convert
−3π
4 to degree measure.
19a. Find and explain what the value of cos 120⁰ is.
19b. Find and explain what the value of sin 120⁰ is.
19c. Find and explain what the value of cos -120⁰ is.
19d. Find and explain what the value of cos
2π
3
is.
20a. Find the value of tan θ in the diagram:
20b. Find the value of cos θ in the diagram:
20c. Find the value of sin θ in the diagram:
20d. Find the value of tan α in the diagram:
20e. Find the value of sin φ in the diagram:
What is the Law of Sines?
What is the Law of Cosines?

10.1
10.2
Label each triangle with the formula that you would use to find the missing sides or angles:
21a. Find the missing angles and sides in the given triangle:
21b. Use the given diagram to explain why two different angles can have the same sine. Then explain how that affects the Law of Sines.
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________

9.1
7.1
7.2
22a-f. Label each graph below as the matching trigonometric functions. Don’t forget that each picture may have more than one answer because of phase shifts!
1 + csc x
csc x
23a-d. Simplify each of the given expressions: sec x csc x
1 . csc x – sin x sec x tan x cos 2 x
1-sin x sin 2 x-tan 2 x

10.6
10.6
10.3
8.1
8.4
6.5
24a. If sin θ =
3
5
and cos θ =
−4
5
, then what is the value of tan θ ?
24a. If sin θ =
1
2
24a. If sin θ =
5
13
and cos θ =
24a. If sin θ =
−6
10
and cos θ =
and cos θ =
√3
, then what is the value of tan θ ?
2
−12
13
8
10
, then what is the value of tan θ ?
, then what is the value of tan θ ?
25a. Which of the following is a solution to the equation: cos ( x-
π
3
) =
1
2
?
25b. Which of the following is a solution to the equation: sin ( x-
π
2
) =
1
2
?
25c. Which of the following is a solution to the equation: cos ( x+
π
6
) =
√2
2
?
25d. Which of the following is a solution to the equation: cos ( x-
2π
3
) =
−1
2
?
26a. What is the magnitude of the vector <2, -4> ?
26b. What is the magnitude of the vector <-3, -4> ?
26c. What is the magnitude of the vector 3i + 2j ?
27a. Convert the rectangular coordinates ( -2, 4 √3) to polar coordinates .
27b. Convert the rectangular coordinates ( -2, 4 √3) to polar form .
27c. Convert the rectangular form 2 + 3i to polar form.
28a. What is the direction of the vector ‹
3√2
5
,
√2
5
› ? What is the magnitude of that vector?
28b. What is the direction of the vector ‹
3√2
5
,
−√2
5
› ? What is the magnitude of that vector?
28c. What is the direction of the vector 3i – 4j ? What is the magnitude of that vector?

10.
6A
10.3
29a. If z
1
= 3 (cos 25⁰ + I sin 25⁰) and z
2
= 2 (cos 95⁰ + I sin 95⁰), then what is z
1 ∙
z
2
?
29b. What is z
1 ∙
z
1
?
29C. What is z
1
4 ?
29a. If z
1
= 3 (cos
π
3
+ I sin
π
) and z
2
= 2 (cos
3
2π
5
+ I sin
2π
5
), then what is z
1 ∙
z
2
?
29b. What is z
2 ∙
z
2
?
29C. What is z
1
3 ?
30a. A 1200 pound rock is on a ramp that makes a 20 0 angle with horizon. Find the force necessary to keep the rock from rolling down the ramp.
30b. A 700 pound truck is on a ramp that makes a 12 0 angle with horizon. Find the force necessary to keep the truck from rolling down the ramp.
The Final exam will also include Chapters 11(Polar Coordinates, 12 (Limits) and Partial Fraction Decomposition
(pages 838-841). While this guide attempts to cover the subjects of the Final Exam, students should be aware that they are responsible for all material covered during the semester. There will be a formula sheet provided during the final exam.