Find the value of : sin 47 (degrees) + sin 61 (degrees) - sin 11 (degrees) - sin 25 (degrees)

Question

anonymous · Answer

set the calculator to degrees and start pressing buttons

mathslover · Answer

lol @1on1 , that's a shortcut but I do want to do that without *calculator*

anonymous · Answer

Sorry, that will require much more thought from me !

mathslover · Answer

No problem! @sasogeek any suggestions, if no then I have only 1 .

mathslover · Answer

Not suggestion but an idea infact.

sasogeek · Answer

use the calculator to find their actual values and do normal addition... that's if u want to do some work... if not, u may use the calculator to find the whole answer.

mathslover · Answer

hmn quite hard if calculator is not allowed.

sasogeek · Answer

earlier i thought it was sin(A+B)-sin(A-B) sort of question but it's not, direct solution with the calculator is the way forward :) unless u know those values off the top of ur head xD

mathslover · Answer

xD thanks though

sasogeek · Answer

i do not wish to confuse you, but you may want to read this, http://www.trans4mind.com/personal_development/mathematics/trigonometry/sumProductCosSin.htm#Sum_of_Sine_and_Cosine

anonymous · Answer

@mathslover  Do u knw the Value of Sin18 and cos36

anonymous · Answer

SinA + SinB = 2Sin (A+B)/2 . Cos (A-B)/2...Use this

mathslover · Answer

@Yahoo! and @sasogeek this was my main idea.

mathslover · Answer

Let me try again to find out the answer through the formula of sina + sinb

mathslover · Answer

OK so if I remember the values of : cos 36 degrees and sin 18 degrees then I am getting cos 7 degrees.

mathslover · Answer

cos Here is it how I did that : 

$$\large{\sin 47 + \sin 61 = 2 \sin 54 \cos 7 }$$
^that theta(s) are in degrees. 

similarly : 

$$\large{-(\sin 11 + \sin 25) = -( 2\sin 18 \cos 7)}$$ 

from the above we get : $2\cos 7 ( \sin 54 - \sin 18 )$ 

$2\cos 7 ( 2\cos 36 \sin 18)$

$4\cos 7 (\frac{\sqrt{5}+1}{4} \times \frac{\sqrt{5}-1}{4})$

$\cos 7$

That is it! Is it correct? @sasogeek @Yahoo!

anonymous · Answer

Yup...thats wat i also Got

anonymous · Answer

2Sin54.cos7 - 2sin18cos7


2cos7 ( sin54 - sin18)

sin54 = cos 36

2cos7(cos36 - sin18)

2cos7( (sqrt5 + 1)/2 - (sqrt5-1)/2)

= cos7

anonymous · Answer

Sorry   2cos7( (sqrt5 + 1)/4 - (sqrt5-1)/4)

mathslover · Answer

np, thanks a lot for your help yahoo.

anonymous · Answer

Welcome....)...

anonymous · Answer

To..Be honest..U Did All the Hard Work..)