# Trigonometry Problems

• May 24th 2008, 04:15 AM
Liquidpyro911
Trigonometry Problems
Here are a few Trig problems that I am having trouble with. Any help is greatly appreciated...

-Andrew

1. How many times more intense is a 7.1 richter earthquake than a 6.2 richter quake.
R = log (I/O)

2. Evaluate the value of each indicated trig function (SHOW ALL WORK). I can do this one, but I always forget to show all of my work...

If cos(B) = 4/5, and 3pi/2 < B < 2pi... Find Cot(-B), Cos(2B), and sin(2B)

3. Answer the question by decoding the message, Show all work...
What was trig?
Message encoded using A= [2 5]
1 3
38,105,23,69,21,62,20,60,21,55,2,6,29,82,40,100,36 ,93,20,60,31,84,29,82
• May 24th 2008, 07:14 AM
TheEmptySet
Quote:

Originally Posted by Liquidpyro911
Here are a few Trig problems that I am having trouble with. Any help is greatly appreciated...

-Andrew

1. How many times more intense is a 7.1 richter earthquake than a 6.2 richter quake.
R = log (I/O)

We need to solve the above equation for intensity

$\displaystyle 10^R=\frac{I}{O} \iff I =O \cdot 10^R$

Now pluging in our values gives

$\displaystyle I_1=O \cdot 10^{7.1}$

$\displaystyle I_2=O \cdot 10^{6.2}$

Now we divide the two

$\displaystyle \frac{I_1}{I_2}=\frac{O \cdot 10^{7.1}}{O \cdot 10^{6.2}} \approx 7.94$

Please show us what you have tried for the other two. :D
• May 24th 2008, 07:30 AM
Liquidpyro911
I finished #2, but I just have no idea how to do number 3...

Thanks for the help with the first one... btw...
• May 24th 2008, 10:49 AM
Reckoner
Quote:

Originally Posted by Liquidpyro911
I finished #2, but I just have no idea how to do number 3...

Thanks for the help with the first one... btw...

I'm assuming the matrix for number 3 is

$\displaystyle \left[\begin{array}{cc} 2 & 5\\ 1 & 3 \end{array}\right]$.

It seems to me that the message was encoded using this simple algorithm:

1. Convert all letters to numerical values, with 0 = space, 1 = A, 2 = B, etc
2. Store each pair of values in a 1×2 row matrix
3. Multiply each uncoded row matrix on the right by $\displaystyle A$ to form a coded row matrix
4. List the values in the coded row matrices, in order and without the matrix notation, to form the coded message

All you have to do is repeat this process in reverse (hint: you will need to find $\displaystyle A^{-1}$).