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.)

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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
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\[1'={\frac{1}{60}}^{\circ}\] \[180^{\circ}=\pi \space rad\]\[1^{\circ}=\frac{\pi}{180} \space rad\]\[{\frac{1}{60}}^{\circ}=?? \space rad\]
What do you think?
I get 0.0002908...

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How much you are getting?
Let me check
Okay.
and what is the answer they've given?
Not mentioned.
I mean, it says "3 sig figs" and that would give me basically 0?
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
So... scientific notation?
What exactly did you write for your answer?
I'd done it wrong before lol
So your found your mistake?
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
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
*puts in 0.000291* *gets right answer* WHAT.
THE HECK.
I see your mistake now, why are you writing 2.91?? Write the answer that we found! 0.000290 - upto 3 significant figures!
291. I had to round.
It's right.
ahh, see
I'd put some entirely diff # before. lol
anyways for your next part we have
2π+3π/4 didn't work
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 \[a=10800\]
Did you get all that?
Oh dear
10800??
yep Here we have a=10800 \[{\frac{1}{60}}^{\circ}=\frac{\pi}{180} \times \frac{1}{60} \space rad\]
why is a 10800?
ok first do you understand that \[1^{\circ}=\frac{\pi}{180} \space rad\]
Yes.
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
oh lol.
And yes.
Now read my explanation above of how to convert it into terms of 2pi, i've written it above
I got lost.
o-o
Ok i'll try again
Suppose you have a fraction of the form \[\frac{\pi}{a}\]
You can multiply it with 1, makes no difference, I'll write that just to create some clarity \[\frac{\pi(1)}{a}\]
following so far?
Got it so far.
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
so far good?
Yep
To further illustrate, I'll distribute the pi and see what we get \[\frac{\pi(1+b-b)}{a}=\frac{\pi+b \pi-b \pi}{a}=\frac{\pi}{a}\]
So it makes no difference
Sorry; I'm tired so I take a while to process this stuff haha
Next we will split our fraction into 2 fractions \[\frac{\pi(b+1-b)}{a}=\frac{\pi b+\pi(1-b)}{a}=\frac{\pi b}{a}+\frac{\pi(1-b)}{a}\]
Just keep responding if you are following, when you're not, let me know
Okay.
Actually... um, can you just tell me what's wrong with the equation I put in?
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
Sure, I'll see
Where's your attempt ??
Eh ?
You want me to check what you've done wrong for question 2, right?so let me see your work
http://icecream.me/3db4b88a7128b83b79b4db0bb933e6c5
Oh I see, so they want you to express \[\frac{7\pi}{4}\] I thought they meant the answer you got from 1st part
You've expressed it in terms of pi not 2pi
What number do you think when divided by 4 gives 2?
?
\[\pi=\frac{4\pi}{4}?\rightarrow \pi+\frac{3\pi}{4}=\frac{4\pi}{4}+\frac{3\pi}{4}=\frac{7\pi}{4}\]
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?
I want to express it in terms of pi?
Nope, check your question
! FFFFFF
So then:\[2\pi-\frac{\pi}{4}\]
yep!
BAH I feel dumb
What about part 3?
You didn't post any part 3
oh I see it now
You sure? :p
xD
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 \[\theta \approx 0.000291\]\[1 \space nautical \space mile = 4000 \times 0.000291 \space miles\]
Whut.
Gimme a sec lol
We are given 1 minute in the question, not 1 degree
Okay I got what you said.
But I'm not sure where to go from here.
well just calculate the product and you'd get the relation between a nautical mile and miles
okay
1.164 is what I got
Should be it
Alright
Thanks! :D
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
nvm I got it right now
Extremely sorry I didn't notice, I was studying myself, but I'm glad you got it anyway.
xD
S'alright. I think I'm good now, you don't have to stay :]

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