We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
2421
9
avatar

sin 105 - sin 15

 Nov 17, 2014

Best Answer 

 #9
avatar+101741 
+40

Thanks Heureka,

I have to think about that one too Chris :)

It is too late now :))

 Nov 18, 2014
 #1
avatar+17774 
+5

√(2) / 2

 Nov 18, 2014
 #2
avatar+101741 
+10

 

NOW GENO - I know I am a real expert at making a mountain out of an mole hill BUT how did you do it with no working?   

 

$$\\sin 105 - sin 15\\
=sin(180-105)-sin15\\
=sin75-sin15\\
=cos15-sin15\\
=cos(45-30)-sin(45-30)\\
=cos45cos30+sin45sin30-[sin45cos30-cos45sin30]\\
=sin45cos30+sin45sin30-sin45cos30+cos45sin30\\
=sin45sin30+sin45sin30\\
=2sin45sin30\\
=2\times\frac{1}{\sqrt2}\times\frac{1}{2}\\
=2\times\frac{1}{\sqrt2}\times\frac{1}{2}\\
=\frac{1}{\sqrt2}\\
=\frac{\sqrt2}{2}\\$$

.
 Nov 18, 2014
 #3
avatar+101149 
+5

Yeah....the way geno came up with that answer is a "sin"

 

 Nov 18, 2014
 #4
avatar+101741 
+5

Hi Chris,

I am looking forward to Geno response   LOL

Maybe there is some 'obvious' method.  But it will make me feel less stupid if you can't 'see' it either,  :))

 Nov 18, 2014
 #5
avatar+101149 
+5

Don't feel too stupid......I don't see the "trick," either......maybe there is some "identity" of which we are unaware....!!!

 

 Nov 18, 2014
 #6
avatar+22290 
+5

sin 105 - sin 15

$$\sin{( 105\ensurement{^{\circ}} )} - \sin{( 15\ensurement{^{\circ}} ) } \\
=\sin{( 90\ensurement{^{\circ}} + 15\ensurement{^{\circ}} )} - \sin{( 15\ensurement{^{\circ}} ) } \\
= \underbrace{\sin{( 90\ensurement{^{\circ}} ) }}_{=1}\cos{( 15\ensurement{^{\circ}} ) }+\underbrace{\cos{( 90\ensurement{^{\circ}} ) }}_{=0} \sin{( 15 \ensurement{^{\circ}}) }- \sin{( 15\ensurement{^{\circ}} ) }\\
=\cos{(\textcolor[rgb]{1,0,0}{15\ensurement{^{\circ}}} )} - \sin{( \textcolor[rgb]{1,0,0}{15 \ensurement{^{\circ}}}) } \\ \\
\boxed{
=\sqrt{2}\cos{(\textcolor[rgb]{1,0,0}{15\ensurement{^{\circ}}} +45\ensurement{^{\circ}} )}\\
=-\sqrt{2}\sin{(\textcolor[rgb]{1,0,0}{15\ensurement{^{\circ}}} -45 \ensurement{^{\circ}})} \\
=\frac{\sqrt{2}}{2} = 0.70710678119
}$$

.
 Nov 18, 2014
 #7
avatar+101149 
0

How did you get from

cos(15) - sin(15)    to

√2cos(15 + 45)   and then to

-√2sin(15 - 45)  ????

 

 Nov 18, 2014
 #8
avatar+22290 
+5

.
 Nov 18, 2014
 #9
avatar+101741 
+40
Best Answer

Thanks Heureka,

I have to think about that one too Chris :)

It is too late now :))

Melody Nov 18, 2014

15 Online Users

avatar