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Butterfly16
Find an exact value. cos 15° Options: A) sqrt 6 + sqrt 2 / 4 B) - sqrt2 + sqrt 6 / 4 C) - sqrt2 - sqrt 6 / 4 D) - sqrt6 + 1 / 4
A) \[ \frac{ \sqrt{6}+\sqrt{2} }{ 4 } \] B) \[\frac{ -\sqrt{2} +\sqrt{6} }{ 4 }\] C) \[\frac{ -\sqrt{2} - \sqrt{6} }{ 4 }\] D) \[\frac{ -\sqrt{6} +1}{ 4 }\]
cos(a-b)=cosa cosb + sina sin b you know? if ok cos (45-30)= cos45 cos 30 +sin 45 sin 30
where did you get all the numebrs?
|dw:1357845575004:dw| I dont get what you mean !
But its for cos 15° ?
It is an unknown angle you have to make it bu known angle
you know that formula? if yeah put the numbers in it you will have answer (a)
I think I got it. Can you help with another?
Also, you can use \(\cos^2\frac x 2=\frac{1+\cos x}2\).
@klimenkov Can you help with this one, pelase? Write the expression as either the sine, cosine, or tangent of a single angle. \[\cos(\frac{ \pi }{ 5 }) \cos(\frac{ \pi }{ 7 }) + \sin (\frac{ \pi }{ 5}) \sin (\frac{ \pi }{ 7 })\]
as "klimenkov " says you can use that formula shuch the way i draw|dw:1357846727839:dw|
cos(π/5)cos(π/7)+sin(π/5)sin(π/7)=cos (π/5-π/7) by the formula AS i sayd before cos (a+b)= cos a cos b-sin a sin b
so would the cos (a+b) be pi/5+pi/7?
No. It will be \(\cos(\frac\pi5-\frac\pi7)\) as @amoodarya said. Hope you can do this subtraction.
no i think that you get it cos (a+b)= cos a cos b-sin a sin b cos (a-b)= cos a cos b+sin a sin b but 2pi/35 is unknown angle
\[\cos(\frac{ \pi }{ 5 }+\frac{ \pi }{ 7 })\] is 2pi/35? Can you show me how to fill in the formula? I think it'd make it easier for me.
cos (a-b)= cos a cos b+sin a sin b a=pi/5 b=pi/7
cos (pi/5-pi/7)= cos (pi/5) cos (pi/7)+sin (pi/5) sin (pi/7) ?
So the answers 2pi/35?
No. The answer is \(\cos(\frac{2\pi}{35})\).
That's what I said?
You said this without cosine.