Question

cot(-105degrees 10'15")

Answer 1

@campbell_st

Answer 2

so you are finding

\[\cot(-105^o 10' 15")\]

is that correct..?

Answer 3

yes

Answer 4

Ok, so the problem is to convert the angle to units of degrees only, right?

Answer 5

the directions say determine each value. round to the nearest four decimal places

Answer 6

Yes, but I'm asking where is your difficulty
I assume you may a calculator for cot() but before you can do that you have to convert the degree to angles. do you know how to do that?

Answer 7

i do not. and I do not have a calculator

Answer 8

ok, so first thing first. let's convert to degrees. What you see here is degrees + minutes + seconds.
Yes I know it's a little confusing because 'minutes' and 'seconds' are time units and not angles.
Well, not exactly, they are also angle units. A a single degree divides into 60 'minutes', similar to how hour divides into 60 minutes.
A minute divides into 60 seconds, just like with time.
So our angle is \(-105^\circ 10'15''\) which means we have a negative angle of 105 degrees, 10 minutes and 15 seconds

Answer 9

But we know each minute is \(\frac{1}{60}\) degree. so 10 minutes become \(\frac{10}{60}\) degrees which simplifies to what?

Answer 10

1/6?

Answer 11

yes. now we have 15 seconds. but a second is \(\frac{1}{60}\) minute, and a minute is \(\frac{1}{60}\) degree.. so a second is really \(\frac{1}{60} \cdot\frac{1}{60} = \frac{1}{3600}\) degree. so 15 seconds will be what?

Answer 12

15/60

Answer 13

15 seconds would be 15/60 minutes. but we want to find how many 'degrees' it is. so we say, a minute gets inside a degree 1/60 times. so if we have 15/60 minutes, it's just like 15/60 * 1/60 degrees so that would be 15/(60*60) = 15/3600
Makes sense?

Answer 14

yeahh

Answer 15

ok, simplify that as well, what would that be?

Answer 16

1/240

Answer 17

exactly =)
So we have:
$$
-105^\circ10'15'' = -(105 + \frac{10}{60} + \frac{15}{3600})^\circ = -(105 + \frac{1}{6} + \frac{1}{240})^\circ
$$

Answer 18

Now we have to sum it up and calculate the cot() using a calculator. you said you don't have a calculator but there are plenty of them online:
http://web2.0calc.com/

Answer 19

So first, let's sum it up 105 + 1/6 + 1/240 becomes what?

Answer 20

0.2711?

Answer 21

well no. try again

Answer 22

25241/240?

Answer 23

That will work too =)

Answer 24

okay

Answer 25

105.1708

Answer 26

Ok, good. now we had a negative angle so that is really -105.1708

Answer 27

now we need to calculate cot() for this angle. make sure the calculator is in mode of degrees and not radians when you do it

Answer 28

0.2711

Answer 29

Ye, right =)
I thought you gave me that result before for the angle itself, sorry =)

Answer 30

thanks. can you help me with some more?

Answer 31

ok, what do you need?

Answer 32

If f is any function with a period of 6, determine the period of each related function.
A: y=f(x+1)
B: y=f(1/2 x)
C: y=f(3c)+7

Answer 33

ok, so I assume it is meant to be 3x and not 3c at the last one. let's see
Are you familiar with the idea of period?

Answer 34

yeah sorry it is suppose to be x. i'm kind of familiar with it

Answer 35

ok, so a periodic function has the exact same behavior every period. that means that no matter what point we pick on the function, if we add or remove one 'period' from that point we get the exact same value.
For example, sin() and cos() have period of \(360^\circ\) or \(2\pi\) in radians because no matter what value you pick \(sin(x) = sin(x + 360^\circ)\)
By adding 360 you get the exact same value, just a period after.

Answer 36

makes sense

Answer 37

So we can see that the exact value of \(x\) doesn't matter. it would work both for x=0 and x=30 in the same way. So in the first example A, we can see that the only difference from the original function f() is that x is incremented by one first. so if it was x=0 now it is x=1. if it was x=5 now it is x=6..
But we already know that it doesn't matter, we just shift all the values of x, but the period is the same.

Answer 38

We can also examine it. we know that f(x) = f(x+6) because f() has period of 6.
Now in A we have
$$
y(x) = f(x+1)\\
y(x + 6) = f(x + 6 + 1) = f( (x+1) + 6) = f(x+1) = y(x)
$$

Answer 39

makes sense?