7-1

Review of 7-1

This week I'm going to do a review on lesson 7-1 since we've been doing trig review all week. In this lesson, we learn how to convert degrees to radians, radians to degrees, degrees to minutes and seconds, and minutes and seconds to degrees. We also learned how to find co-terminal angles.

- To convert degrees to radians: degrees x pi/180 (In the calc, you type degrees/180, and convert to a fraction, then put pi beside it.

- To convert radians to degrees: radians x 180/pi (Pi will cancel out)

- To covert degrees to minutes and seconds: For minutes, you take what is behind the decimal and multiply by 60. Once you get that answer, you take what is behind the decimal and multiply by 60 which will give you your seconds.

- To convert from minutes and seconds to degrees: degrees + min/60 + sec/3600

- To find a co-terminal angle: n +/- 360 degrees

Example 1:

a) convert 315 degrees to radians: 315 degrees x pi/180

= 7pi/4

b) convert -pi/2 to degrees: -pi/2 x 180/pi

= -90 degrees

c) convert 1.32 to degrees, minutes, and seconds: 1.32 x 180/pi

= 75.630 degrees

- .630 x 60 = 37.8 minutes

- .8 x 60 = 48 seconds

= 75 degrees, 37 minutes, 48 seconds

Example 2:

a) Find a positive co-terminal angle to -100 degrees: -100 + 360

= 260 degrees

b) Find a negative co-terminal angle to 500 degrees: 500 - 360(2)

= -220 degrees

Review of Probability

This is simple if you remember the difference between mutually exclusive and not mutually exclusive.

Notes:

If two events are mutually exclusive, then they cannot happen at the same time.

P(A or B) = P(A) + P(B) - P(A & B).

-If the events are not mutually exclusive, then P(A or B) = P(A) + P(B).

Ex 1: A standard deck of cards consists of 52 cards, with 13 cards in each of four suits (clubs, spades, diamonds, and hearts). Clubs and spades are black, and diamonds and hearts are red. The face cards consist of jacks, queens, and kings. Assuming the deck is shuffled properly, what would be the probability that a card is:

• red = 26/52 = 1/2
• A black club = 13/52 =1/4
• blue = 0/52 = 0
• A jack = 4/52 = 1/13

-Sameer

review of matrices,WOOHOO

This week, since we just reviewed trig and took our exam, I’ve decided that I would review the wonderful world of matrices with all of you. So here we go with the blogging and what not.

-A^t means transpose. That simply means switch the rows and columns.
-To add matrices they must be the same dimensions (number of rows and columns)
-To complete scalar multiplication you multiply every entry by the number.

EXAMPlE TIIIIIIIIIIIIME
M= [7 1 5]
[4 3 2]

A. What are the dimensions of the matrix?
2x3 ( There are two rows and three columns )

B. Find m^t
[4 7]
[3 1]
[2 5]

Example TWO:

Add the matrix from the last example and the matrix
[8 3 4]
[6 2 9]

Simply add the corresponding spots.
[7+8 1+3 5+4]
[4+6 3+2 2+9]

The answer would then be:
[15 4 9]
[10 5 11]

So that is how you work with matrices.

--Sarah (:

MORE BLOGS YAY

Lets talk about solving exponents as a variable

1) take the log or ln of both sides

*use ln where there is an e*

2) put into calculator if asked exact values don't get input in a
calculator

EX:
4^x=16
log4^x=log 16
xlog4=log16
x= log16/log4
x=2

BLOGS YAY

cory rules

exponents that are variables

today im showing you how to solve for exponents that is a vairable. the steps are listed below and will be followed with examples to clarify the process.
1) take the log or ln of both sides *use ln where there is an e*
2) put into calculator if asked exact values don't get input in a calculator



EX:
3^x = 12
log 3x = log 12
x= log 12 / log 3
x= 2.26

(the square root of) e^x = 50
ln e^1/2x = ln 50
x= (ln 50 / ln e) *2
x=7.82

Cos(a +/- B) and sin(a +/- B)

Things you need to know:

• cos(a +/- B) = cosa(cosB) -/+ sina(sinB)
• sin(a +/- B) = sina(cosB) +/- cosa(sinB)
• sinx + siny = 2sin(x + y/2) cos(x - y/2)
• sinx - siny = 2cos(x + y/2) sin(x - y/2)
• cosx + cosy = 2cos(x + y/2) cos(x - y/2)
• cosx - cosy = -2sin(x + y/2) sin(x - y/2)

Example 1: Find the exact value of cos75 degrees.

• You will first go to your trig chart to find out what adds to give you 75 for cos.
• Those numbers are 45 and 30.
• You are going to use those numbers in the first formula from above.
• cos(45 + 30) = cos45(cos30) - sin45(sin45)
• Now you plug in what those are from the trig chart.
• (square root of 2/2)(square root of 3/2) - (1/2)(square root of 2/2)
• square root of 6/4 - square root of 2/4
• Final answer: square root of 6 - square root of 2/4

Example 2: sin30(cos15) + cos30(sin15)

• For this problem they give you the two numbers they are adding so you have to replace it with one of the formulas.
• If you look at the problem and the formulas you have from above, it is the same as sin(a + B).
• Now you can replace.
• sin(30 + 15) = sin(45)
• Now that you have gotten an answer, you have to see what sin(45) is on the trig chart.
• sin(45) on the trig chart is square root of 2/2.
• Final answer: square root of 2/2.

-Amber :)