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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

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Covert Radians to Degrees and 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

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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.

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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?

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Commission 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.

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End Behavior

1.  Find the end behavior of the following functions:

(a)  Consider:  y = (x²-2x)/(-x³-5x²+4)
as x goes to ∞, y goes to ?
as x goes to – ∞, y goes ?

(b) Consider y = (2x+1)/(-4x+1)
as x goes to ∞, y goes ?
as x goes to – ∞, y goes ?

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Probability Problem

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.

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