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:

Divide both sides by 360:

Or, if we had divided both sides by 2π we get:

These equations give us our conversion factors…

To convert from degrees to 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:

Example:  Covert 5π/6 radians to degrees:

5π/6 * (180/π) = 900π/(6π) = 150

So, 5π/6 radians = 150 degrees.

# More Trig Solving

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

# Trig problem

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

# Exact Values for Trig Functions

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.

# Word Problem

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.

# Trig solutions

Q:  Find all solutions to the equation in the interval [0, 2pi): sin(2x) – tan(x) = 0

# End Behavior

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 ?