Q : Identify the x-values that are solutions of each multiple choice equation:
1. 8cos x +4 = 0
A. x= 2π/3 , 4π/3
B. x=4π/3, 5π/3
C. x = π/3 , 5π/3
D. x =π/3 , 4π/3
2. 10cos x – 5 √(3) = 0
A. x =5π/6 , 7π/6
B. x = π/6 , 11π/6
C. x = 7π/6 , 11π/6
D. x = π/6 , 7π/6
3. 18cos x – 9 = 0
A. x = 4π/3 , 5π/3
B . x = 2π/3 , 4π/3
C . x = π/3 , 5π/3
D. x = π/3 , 4π/3
Here is what we know:
360° = 2π Radians
Divide both sides by 360:
1° = π/180 Radians
Or, if we had divided both sides by 2π we get:
1 Radian = 180°/π
These equations give us our conversion factors…
To convert from degrees to radians:
degrees * (π/180) = radians
Example: Covert 120 degrees to radians:
120 * π/180 = 120π/180 = 2π/3
So, 120 degrees = 2π/3 radians.
To convert from radians to degrees:
radians * (180/π) = degrees
Example: Covert 5π/6 radians to degrees:
5π/6 * (180/π) = 900π/(6π) = 150
So, 5π/6 radians = 150 degrees.
Q : Find all solutions of the equation in the interval [0, 2pi )
2 cos² x = 13 sin x – 5
(Multiple Choice)
A. π/4 , 3π/4 , 5π/4 , 7π/4
B. π/6, 5π/ 6
C. 3π/4 , 7π/4
D. π/3 , 2π/3 , 4π/3 , 5π/3
Q: Find all solutions of the equation in the interval [0, 2pi )
tan²x – sec x = -1
(MULTIPLE CHOICE)
a. 0
b. pi/4 , 3pi/4 , 5pi/4 . 7pi/4
c. pi/6 , 5pi/6
d. 2pi/3 , pi , 4pi/3
If you are in trigonometry or pre-calculus, the below is something you want to memorize, write down, something! Here is a table with the “exact values” for the important angles we use:
| Degrees | Radians | sin(x) | cos(x) | tan(x) |
| 0 (or 360) | 0 (or 2π) | 0 | 1 | 0 |
| 30 | π/6 | 1/2 | √(3)/2 | √(3)/3 |
| 45 | π/4 | √(2)/2 | √(2)/2 | 1 |
| 60 | π/3 | √(3)/2 | 1/2 | √(3) |
| 90 | π/2 | 1 | 0 | Undefined |
| 180 | π | 0 | -1 | 0 |
| 270 | 3π/2 | -1 | 0 | Undefined |
Remember: If you ever need to find csc, sec, or cot values, they are just reciprocals. Csc is the reciprocal of sin, sec is the reciprocal of cos, and cot is the reciprocal of tan.
Q: Steve Trinter, an electronics salesman, earns a weekly salary plus a commission on sales. One week he sold $4000 in merchandise and was paid $660. The next week his sales totaled $6000, and his pay was $740. Find his weekly salary and his commission rate.
Q: Find all solutions to the equation in the interval [0, 2pi): sin(2x) – tan(x) = 0
1. Find the end behavior of the following functions:
(a) Consider: y = (x²-2x)/(-x³-5x²+4)
as x goes to infinity, y goes to ?
as x goes to – infinity, y goes ?
(b) Consider y = (2x+1)/(-4x+1)
as x goes to infinity, y goes ?
as x goes to – infinity, y goes ?
Q: Solve: log(5x − 7) − log(4x − 5) = 0
Q: Problems of sexual harassment recieved much attention in recent years. In one survey, 420 workers (240 of whom are men) considered a friendly pat on the shoulder to be sexual harassment, whereas 580 workers (380 of whom are men) did not consider it to be a form of harassment. Find the probability of randomly selecting a man or someone who does not consider a pat on the shoulder to be a form of sexual harassment.
Stacey Vaughn, Math Tutor 