# Thread: Determine the exact value of sin (x + 30)

1. ## Determine the exact value of sin (x + 30)

If $x^\circ$ is an acute angle such that $Tan x^\circ = 4/3$, Determine the exact value of sin (x + 30).

To tackle this I initially wanted to do $tan^-^1(4/3)$ and then sub that into the value as x but it doesn't seem the correct procedure for the question.

Thanks,

Kris

2. ## Re: Determine the exact value of sin (x + 30)

Originally Posted by Krislton

If $x^\circ$ is an acute angle such that $Tan x^\circ = 4/3$, Determine the exact value of sin (x + 30).
Hint: $\sin( x^\circ)=\frac{4}{5}$

3. ## Re: Determine the exact value of sin (x + 30)

Originally Posted by Plato
Hint: $\sin( x^\circ)=\frac{4}{5}$
thanks for the hint, does that mean the solution is $sin^-^1 (\frac{4}{5}) +30 = 83.13...^\circ$

4. ## Re: Determine the exact value of sin (x + 30)

Use the sum identity
sin(A+B) = sinA cosB + cosA sin B
sin (x+30) = sin x cos 30 + cos x sin 30
= [sqr 3 / 2] * sin x + cos x * 1/2 etc.

5. ## Re: Determine the exact value of sin (x + 30)

Originally Posted by ibdutt
Use the sum identity
sin(A+B) = sinA cosB + cosA sin B
sin (x+30) = sin x cos 30 + cos x sin 30
= [sqr 3 / 2] * sin x + cos x * 1/2 etc.
Hi,

Thanks for the input but I dont get your third line statement " = [sqr 3 / 2] * sin x + cos x * 1/2 etc." Please explain

6. ## Re: Determine the exact value of sin (x + 30)

Originally Posted by Krislton
Hi,

Thanks for the input but I dont get your third line statement " = [sqr 3 / 2] * sin x + cos x * 1/2 etc." Please explain
$\cos(30)=\frac{\sqrt{3}}{2}$ and $\sin(30)=\frac{1}{2}$

These are standard results you should memorise or even better, learn how to derive (consider the right angled triangle with lengths $1,\sqrt3,2$ and angles $30,60,90$)

7. ## Re: Determine the exact value of sin (x + 30)

Originally Posted by Krislton
Thanks for the input but I dont get your third line statement " = [sqr 3 / 2] * sin x + cos x * 1/2 etc.
If you do not understand this formula $\sin(A+B) = \sin(A) \cos(B) + \cos(A) \sin( B)$ then you have no business trying this question.

Now $\sin(x^o)=\frac{4}{5}~~\cos(x^o)=\frac{3}{5}$. With those you can complete the question.

If you can't, then you need live tutorial help.

8. ## Re: Determine the exact value of sin (x + 30)

Originally Posted by Gusbob
$\cos(30)=\frac{\sqrt{3}}{2}$ and $\sin(30)=\frac{1}{2}$

These are standard results you should memorise or even better, learn how to derive (consider the right angled triangle with lengths $1,\sqrt3,2$ and angles $30,60,90$)
I understand when its written in LaTeX, my brain just couldn't process it for some reason written in normal text. thanks!

9. ## Re: Determine the exact value of sin (x + 30)

Originally Posted by Plato
If you do not understand this formula $\sin(A+B) = \sin(A) \cos(B) + \cos(A) \sin( B)$ then you have no business trying this question.

Now $\sin(x^o)=\frac{4}{5}~~\cos(x^o)=\frac{3}{5}$. With those you can complete the question.

If you can't, then you need live tutorial help.
Thanks for your belittling comment. I thought these forums were here to try to help people to try to understand the problems they've been faced with, not to state whether someone has business in said subject. Yes I very much struggle with my maths but when my degree relies on the skill I very much need to improve on, don't you think it would be more helpful to someone to support then to have a moral lowering comment being posted. I find I learn best by completed examples. Anyway, thanks for all your input but as of now, I don't know how to get the solution so I will try find "live tuition" from now.

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### sin(x)=sin(x-30)

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