Small angle (1 Viewer)

[atakach99]

Given x is small, show that

sin (pie/3 + x) approximatly equal to 1/2(square root 3 + x)

 

[lyounamu]

Given x is small, show that

sin (pie/3 + x) approximatly equal to 1/2(square root 3 + x)

sin (pi/3) = (square root of 3)/2
Therefore, L.H.S. = sin (pi/3 + x)
~ 1/2 (square root of 3 + x)
= RHS (if you look at the calculator, the value of x will be halved in most cases).

This question is hard to show. I cannot think of a better way but using a calculator.

I would seriously like to use the formula that sin (x+y) = sin(x)cos(y) + cos(x)sin(y) but I can't because that is the Mathematics Extension 1 topic.

 

[atakach99]

ohh ok thnks man
ur a genius

 

[tommykins]

I'd use limits as x -> 0 and sub x = 0 in.

 

[lyounamu]

I'd use limits as x -> 0 and sub x = 0 in.

Oh. That's smart!!! I better learn how to think outside the norm.

L.H.S.=lim x -> 0 sin (pi/3 +x)
= sin (pi/3 +0)
= sin (pi/3)
= (square root of 3)/2
= 1/2 (square root of 3 + 0)
= 1/2 (square root of 3 + x) (since x = 0 in this case).
= R.H.S

Thanks to tommykins for great advice. I would not have solved it without the advice he gave me.

 

[Iruka]

sin (pi/3 + x) = sin(pi/3)cos(x) + cos(pi/3) sin(x)

If x is small, sin(x) approx = x, cos(x) approx = 1,

so sin(pi/3 + x ) approx = sqrt(3)/2 + x/2.

Its useful to remember that if x is small, sin(x) approx = tan (x) approx = x. (The tangent line to both these curves at x=0 is y=x.)

 

[atakach99]

ok guys i know this is a sill question sorry

evaluate, correct to 3 decimal places

sin 0.045

when i type it into my calculator i get a weird answer can somebody show me how to do this question plz

 

[lyounamu]

ok guys i know this is a sill question sorry

evaluate, correct to 3 decimal places

sin 0.045

when i type it into my calculator i get a weird answer can somebody show me how to do this question plz

sin 0.045 = 0.0449848140...
= 0.045 (make sure it is in the radian mode because they would not give you 0.045 degrees!)

 

[atakach99]

i feel so embaressed right now

 

[lyounamu]

i feel so embaressed right now

I know few kids in my class who don't even know whether they have to use radian or degree mode. So, it's quite common.

Don't worry, there are heaps of people who make stupid mistakes in HSC due to this.

 

[Forbidden.]

i feel so embaressed right now

Lol I don't like limit theorems in uni maths either.

 

[tommykins]

Oh. That's smart!!! I better learn how to think outside the norm.

L.H.S.=lim x -> 0 sin (pi/3 +x)
= sin (pi/3 +0)
= sin (pi/3)
= (square root of 3)/2
= 1/2 (square root of 3 + 0)
= 1/2 (square root of 3 + x) (since x = 0 in this case).
= R.H.S

Thanks to tommykins for great advice. I would not have solved it without the advice he gave me.

You should take note of which question level it is, since this is 2unit - it only requires a simple method.

 

[lyounamu]

You should take note of which question level it is, since this is 2unit - it only requires a simple method.

Don't you use this level of working out in Mathematics?

I remember doing this kind of question back in Preliminary year.

 

[tommykins]

Don't you use this level of working out in Mathematics?

I remember doing this kind of question back in Preliminary year.

It really depends on how you think about it. Yeah this was in the prelim year course, it's mainly just simplify an expression and sub in the given limit. It gets harder as yuo go however.

I had a question in my exam (3unit) where it was -

lim x -> pi/4 (sinx - cosx)/(x-pi/4)

In which I had no idea where to start, you couldn't sub in x = pi/4 since it makes the denominator 0 which then leads to it being undefined.

If you feel like having a go at it, post your answer here and I'll tell you if you're right or not

 

[lyounamu]

It really depends on how you think about it. Yeah this was in the prelim year course, it's mainly just simplify an expression and sub in the given limit. It gets harder as yuo go however.

I had a question in my exam (3unit) where it was -

lim x -> pi/4 (sinx - cosx)/(x-pi/4)

In which I had no idea where to start, you couldn't sub in x = pi/4 since it makes the denominator 0 which then leads to it being undefined.

If you feel like having a go at it, post your answer here and I'll tell you if you're right or not

Came back from dinner, looked at the question, now I feel my stomach churning my food clearly.

I don't get it actually. But let me try.

EDIT: I think the answer is 0 somehow.

 

[tommykins]

Came back from dinner, looked at the question, now I feel my stomach churning my food clearly.

I don't get it actually. But let me try.

EDIT: I think the answer is 0 somehow.

Hint - rewrite the numerator sinx - cosx in a different form.

 

[lyounamu]

Hint - rewrite the numerator sinx - cosx in a different form.

I already did. I wrote that in t-formula. Did I have to write that in other form? (like sinx = 2(sinx/2)cos(x/2)?)

 

[tommykins]

I already did. I wrote that in t-formula. Did I have to write that in other form? (like sinx = 2(sinx/2)cos(x/2)?)

Lol, just do any method you want, although the solution I have are pretty ridiculous and I was "wtf?" when I looked at it.

 

[atakach99]

ok this one is seems easy but everytime i try it i get a different answer from the back of the book

Find the diameter of the sun to the nearest kilometre if its distance from the earth is 149000000 km and it subtends an angle of 31 ' at the earth

plz help
thnkss

 

[lyounamu]

Lol, just do any method you want, although the solution I have are pretty ridiculous and I was "wtf?" when I looked at it.

I somehow need to get rid of the bottom one (or change it) so that I can work it out. It's not as easy as it looks like. I bloody used the t-formula and it gets more complicated.....