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New and improved!  Bookmark the new link and start asking questions over there!

There is still free help available, as well as some new features to check out.

Thanks,

Stacey

Exact values & multiple quadrant answers

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

Covert Radians to Degrees & Convert Degrees to Radians

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.

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.

Venn Diagram Word Problem

Q:  Superburger sells hamburgers with the choice of ketchup, mustard and relish. One day they sold 256 hamburgers; 140 had mustard, 140 had ketchup, 84 had ketchup and relish, 62 had mustard but no relish, 68 had ketchup and mustard, 38 had all three condiments and 20 had none.

(a) The number sold with relish only is?

(b)The number sold with no relish is?

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 ?