kittiwitti1
  • kittiwitti1
SUBJECT TO EDITING. Trig questions: #1: Use 3.1416 for π unless your calculator has a key marked π. Use a calculator to convert 1' (1 minute) to radians to three significant digits. #2: Write the angle as a difference involving 2π. For example, 5π/3 = 2π − π/3. 7π/4 #3: If a central angle with its vertex at the center of the earth has a measure of 1', then the arc on the surface of the earth that is cut off by this angle (known as the great circle distance) has a measure of 1 nautical mile (see the figure below). Find the number of regular (statute) miles in 1 nautical mile to the nearest hundredth of a mile. (Use 4,000 miles for the radius of the earth.)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[1'={\frac{1}{60}}^{\circ}\] \[180^{\circ}=\pi \space rad\]\[1^{\circ}=\frac{\pi}{180} \space rad\]\[{\frac{1}{60}}^{\circ}=?? \space rad\]
anonymous
  • anonymous
What do you think?
kittiwitti1
  • kittiwitti1
I get 0.0002908...

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anonymous
  • anonymous
How much you are getting?
anonymous
  • anonymous
Let me check
kittiwitti1
  • kittiwitti1
Okay.
anonymous
  • anonymous
and what is the answer they've given?
kittiwitti1
  • kittiwitti1
Not mentioned.
kittiwitti1
  • kittiwitti1
I mean, it says "3 sig figs" and that would give me basically 0?
anonymous
  • anonymous
Your answer is absolutely correct, you can eve google "minutes to radian conversion" I think zeros after a decimal don't count as significant unless they are after some other number, I might be remembering that wrong though
kittiwitti1
  • kittiwitti1
So... scientific notation?
anonymous
  • anonymous
What exactly did you write for your answer?
kittiwitti1
  • kittiwitti1
I'd done it wrong before lol
anonymous
  • anonymous
So your found your mistake?
kittiwitti1
  • kittiwitti1
No... I'm not sure if this is the right answer, so I'd have to check and make sure. I'm not sure how many attempts I have left x_x
anonymous
  • anonymous
Oh, if you are giving an online test/exam, they sometimes require you to write in a particular way, but mathematically your answer is 100% correct
kittiwitti1
  • kittiwitti1
*puts in 0.000291* *gets right answer* WHAT.
kittiwitti1
  • kittiwitti1
THE HECK.
anonymous
  • anonymous
I see your mistake now, why are you writing 2.91?? Write the answer that we found! 0.000290 - upto 3 significant figures!
kittiwitti1
  • kittiwitti1
291. I had to round.
kittiwitti1
  • kittiwitti1
It's right.
anonymous
  • anonymous
ahh, see
kittiwitti1
  • kittiwitti1
I'd put some entirely diff # before. lol
anonymous
  • anonymous
anyways for your next part we have
kittiwitti1
  • kittiwitti1
2π+3π/4 didn't work
anonymous
  • anonymous
You want to express the following fraction in terms of 2pi \[\frac{\pi}{10800}\] So if you were to somehow split the numerator to express it as a sum of 2 fractions, you'd want 1 of the fractions to have a numerator of 2 times the denominator so that you get 2pi upon cancelling \[\frac{\pi}{a}=\frac{\pi(1)}{a}=\frac{\pi(1+b-b)}{a}=\frac{b \pi+(1-b)\pi}{a}=\frac{b \pi}{a}+\frac{(1-b)\pi}{a}\] b is any arbitrary constant, we will choose b such that \[b=2a\] So substituting we get \[\frac{2a \pi}{a}+\frac{(1-2a)\pi}{a}=2\pi+\frac{(1-2a)\pi}{a}\] Here we have \[a=10800\]
anonymous
  • anonymous
Did you get all that?
anonymous
  • anonymous
Oh dear
kittiwitti1
  • kittiwitti1
10800??
anonymous
  • anonymous
yep Here we have a=10800 \[{\frac{1}{60}}^{\circ}=\frac{\pi}{180} \times \frac{1}{60} \space rad\]
kittiwitti1
  • kittiwitti1
why is a 10800?
anonymous
  • anonymous
ok first do you understand that \[1^{\circ}=\frac{\pi}{180} \space rad\]
kittiwitti1
  • kittiwitti1
Yes.
anonymous
  • anonymous
So now we want to find \[1'={\frac{1}{60}}^{\circ}\] How would you do that?you'd divide by 60 of course! Don't worry, I said that oh dear because you were lagging and I was afraid you may have to leave the question in between
kittiwitti1
  • kittiwitti1
oh lol.
kittiwitti1
  • kittiwitti1
And yes.
anonymous
  • anonymous
Now read my explanation above of how to convert it into terms of 2pi, i've written it above
kittiwitti1
  • kittiwitti1
I got lost.
kittiwitti1
  • kittiwitti1
o-o
anonymous
  • anonymous
Ok i'll try again
anonymous
  • anonymous
Suppose you have a fraction of the form \[\frac{\pi}{a}\]
anonymous
  • anonymous
You can multiply it with 1, makes no difference, I'll write that just to create some clarity \[\frac{\pi(1)}{a}\]
anonymous
  • anonymous
following so far?
kittiwitti1
  • kittiwitti1
Got it so far.
anonymous
  • anonymous
Now, we can add and subtract any number, it will make no difference Suppose we have some equation \[x^2+2x+3=9\] If we add and subtract say, root 7, it will make no difference to the equation overall \[x^2+2x+3+\sqrt{7}-\sqrt{7}=9\] Similarly we add and subtract an arbitrary constant b \[\frac{\pi(1+b-b)}{a}\] We can take b as whatever we want, but there's a particular value of b we desire, I'll show you what value later
anonymous
  • anonymous
so far good?
kittiwitti1
  • kittiwitti1
Yep
anonymous
  • anonymous
To further illustrate, I'll distribute the pi and see what we get \[\frac{\pi(1+b-b)}{a}=\frac{\pi+b \pi-b \pi}{a}=\frac{\pi}{a}\]
anonymous
  • anonymous
So it makes no difference
kittiwitti1
  • kittiwitti1
Sorry; I'm tired so I take a while to process this stuff haha
anonymous
  • anonymous
Next we will split our fraction into 2 fractions \[\frac{\pi(b+1-b)}{a}=\frac{\pi b+\pi(1-b)}{a}=\frac{\pi b}{a}+\frac{\pi(1-b)}{a}\]
anonymous
  • anonymous
Just keep responding if you are following, when you're not, let me know
kittiwitti1
  • kittiwitti1
Okay.
kittiwitti1
  • kittiwitti1
Actually... um, can you just tell me what's wrong with the equation I put in?
anonymous
  • anonymous
Now b can take value we want, right? This is because we can add AND subtract any number from an equation or an expression at the same time So if we were to let \[b=2a\] That is completely valid and allowed, like I said b can take any value
anonymous
  • anonymous
Sure, I'll see
anonymous
  • anonymous
Where's your attempt ??
kittiwitti1
  • kittiwitti1
Eh ?
anonymous
  • anonymous
You want me to check what you've done wrong for question 2, right?so let me see your work
kittiwitti1
  • kittiwitti1
http://icecream.me/3db4b88a7128b83b79b4db0bb933e6c5
anonymous
  • anonymous
Oh I see, so they want you to express \[\frac{7\pi}{4}\] I thought they meant the answer you got from 1st part
anonymous
  • anonymous
You've expressed it in terms of pi not 2pi
anonymous
  • anonymous
What number do you think when divided by 4 gives 2?
kittiwitti1
  • kittiwitti1
?
kittiwitti1
  • kittiwitti1
\[\pi=\frac{4\pi}{4}?\rightarrow \pi+\frac{3\pi}{4}=\frac{4\pi}{4}+\frac{3\pi}{4}=\frac{7\pi}{4}\]
anonymous
  • anonymous
You want to express it in terms of 2pi you are expressing in terms of pi Answer me and you'll solve it, what number when divided by 4 will give u 2?
kittiwitti1
  • kittiwitti1
I want to express it in terms of pi?
anonymous
  • anonymous
Nope, check your question
kittiwitti1
  • kittiwitti1
! FFFFFF
kittiwitti1
  • kittiwitti1
So then:\[2\pi-\frac{\pi}{4}\]
anonymous
  • anonymous
yep!
kittiwitti1
  • kittiwitti1
BAH I feel dumb
kittiwitti1
  • kittiwitti1
What about part 3?
anonymous
  • anonymous
You didn't post any part 3
anonymous
  • anonymous
oh I see it now
kittiwitti1
  • kittiwitti1
You sure? :p
kittiwitti1
  • kittiwitti1
xD
anonymous
  • anonymous
ok so first we have \[r=4000 \space mile\]\[l=1 \space nautical \space mile\]\[\theta=1'=\frac{\pi}{10800} \space rad\] We have the formula |dw:1444468327841:dw| \[l=r \theta\] Where, theta is in radians, very important! so we get \[1 \space nautical \space mile = 4000 \times \frac{\pi}{10800} \space miles\] We already calculated the value of the angle earlier in radians it was about \[\theta \approx 0.000291\]\[1 \space nautical \space mile = 4000 \times 0.000291 \space miles\]
kittiwitti1
  • kittiwitti1
Whut.
kittiwitti1
  • kittiwitti1
Gimme a sec lol
anonymous
  • anonymous
We are given 1 minute in the question, not 1 degree
kittiwitti1
  • kittiwitti1
Okay I got what you said.
kittiwitti1
  • kittiwitti1
But I'm not sure where to go from here.
anonymous
  • anonymous
well just calculate the product and you'd get the relation between a nautical mile and miles
kittiwitti1
  • kittiwitti1
okay
kittiwitti1
  • kittiwitti1
1.164 is what I got
anonymous
  • anonymous
Should be it
kittiwitti1
  • kittiwitti1
Alright
kittiwitti1
  • kittiwitti1
Thanks! :D
kittiwitti1
  • kittiwitti1
Oh, another question @Nishant_Garg Evaluate the following expression when x is π/6. Use exact values. 4 cos(2x + π/3 ) I put the below link and was told it was incorrect: http://icecream.me/740b0853764307a397859eaad1391961
kittiwitti1
  • kittiwitti1
nvm I got it right now
anonymous
  • anonymous
Extremely sorry I didn't notice, I was studying myself, but I'm glad you got it anyway.
kittiwitti1
  • kittiwitti1
xD
kittiwitti1
  • kittiwitti1
S'alright. I think I'm good now, you don't have to stay :]

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