ALGEBRA 2/TRIGONOMETRY
Tuesday, June 21, 2011—1:15 to 4:15 p.m.




4 Expressed as a function of a positive acute angle, cos (−305°) is equal
to
(1) −cos 55° (3) −sin 55°
(2) cos 55° (4) sin 55°

Follow the cosine identity that the cosine of a negative number is equal to the cosine of its positive.
cos(-a) = cos(a)
Find the cos(305). Find the difference between it and the closest factor of 90 degrees that's above it. That is 360. Subtract 305 from 360 and that is 55. That means the cos(305) = cos(55)

...

Man's height / Man's shadow = Building's height / Building's shadow
Convert all to inches
69 / 168 = h / 600, where h is the height of the building.
h = (600)(69) / 168
divide h by 12 to convert to feet again
20.5 ft


Australian bedroom are 2.3 meters which is 7.5 feet
5 feet 11 inches/7 feet = 8 feet/x (mine)
71 inches/84 inches in shadow = 96 inches building height/x
cross multiply 84 inches in shadow X 96 inches building height = 8064
8064/71 = 113.57746478873239436619718309859
Divide 113.57746478873239436619718309859 by 12 = 9.4647887323943661971830985915493

Now, his:

His height/His shadow’s height = 8 feet building’s height / 9.46…………for building’s shadow

X/6.5 feet = 8 feet/9.46………..

X/78 inches = 96 inches/9.46…….

96 inches multiplied by 78 inches = 7488

7488/9.4647887323943661971830985915493 = 791.14285714285714285714285714288

791.14285714285714285714285714288 divided by 12 inches = 65.928571428571428571428571428573

65.928571428571428571428571428573 divided by 12 inches = 5.4940476190476190476190476190478

..

34) 56

Circumference of Circle O = 16p inches.
BC = 3/4 of the length of diameter AD
CE = 4 inches


r = 8 (half of diameter)
d = 16pi/pi = 16

AD = Diameter = 16
BC = 3/4 of AD so, BC is Diameter/4 = 4, since we want
3/4, then 3 X 4 = 12
so, BC is 12 inches
AD is 16 inches
CE is 4 inches
Area = 16(2) + 12(2) = 56 Square Inches.



35) $7,4699.04785 is not the correct answer.
5,583.86 is the correct answer because:



Initial Amount = $5000
Interest Rate = 3.75% = 0.0375
Interest in $s = $5000 X 0.0375 = $187.50
Total Amount after 1 year = $5000 + $187.50 = $5187.50

2nd Amount = $5187.50 X 0.0375 = $194.54125
Total Amount after 2 years = $5187.50 + $194.54125 = $5382.03125

3rd Amount = $5382.03125 X 0.0375 = $201.826171875
Total Amount after 3 years = $5382.03125 + $201.826171875 = $5583.857421875
Which really is $5583.86 if you round it up.

P1: 60/60
p2: 6/6
p3: 3/9
p4: 12/12
= 81/87

Unit Circle

What is the domain of g(x) = square root of X square + 2X - 8???

(1) {x|x greater than or equal to 4 or X is less than or equal to -}
(2) {x|x greater than or equal to 2 or X is less than or equal to -4}

g(x)
= sqrt(x^2 + 2x - 8)
= sqrt((x + 4)(x - 2))

For g(x) to be real, x^2 + 2x - 8 must be >= 0
Thus, (x + 4)(x - 2) >= 0
We have x<= -4 or x>= 2

If you want to check, you can substitute a number less than -4, a number between -4 and 2, as well as a number greater than 2 into x^2 + 2x - 8

Hence, the answer is (2).

How do i solve this trigonometry question which involves Sigma?

Barron's Regents book is not as specific in explaining how to solve several problems.

The Sigma's bottom notation is (i=1), notation above is 8. So it's Sigma E, above is 8, bottom is i = 1 and then (3i - i^2).

I know it's -96, but have no clue how it came to be -96.



ANSWER:
Here's how you do it step by step. :)

Sigma always denotes SUM. Therefore, you have to add all the values of the expression by substituting i = 1 to 8.

For,

i = 1: 3(1) - (1)^2 = 3 -1 = 2
i = 2: 3(2) - (2)^2 = 6 - 4 = 2
i = 3: 3(3) - (3)^2 = 9 - 9 = 0
i = 4: 3(4) - (4)^2 = 12 - 16 = -4
i = 5: 3(5) - (5)^2 = 15 - 25 = -10
i = 6: 3(6) - (6)^2 = 18 - 36 = -18
i = 7: 3(7) - (7)^2 = 21 - 49 = -28
i = 8: 3(8) - (8)^2 = 24 - 64 = -40

Therefore, the sum is: 2 + 2 + 0 + (-4) + (-10) + (-18) + (-28) + (-40) = -96.

Hope this helps.

The roots of the equation 3x^2 - 2x = 6 are?

(1) real, irrational, and unequal
(2) real, rational, and equal
(3) real, rational, and unequal
(4) imaginary

The answer is (3)