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Butterfly16

  • 2 years ago

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

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  1. Butterfly16
    • 2 years ago
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    A) \[ \frac{ \sqrt{6}+\sqrt{2} }{ 4 } \] B) \[\frac{ -\sqrt{2} +\sqrt{6} }{ 4 }\] C) \[\frac{ -\sqrt{2} - \sqrt{6} }{ 4 }\] D) \[\frac{ -\sqrt{6} +1}{ 4 }\]

  2. amoodarya
    • 2 years ago
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    cos(a-b)=cosa cosb + sina sin b you know? if ok cos (45-30)= cos45 cos 30 +sin 45 sin 30

  3. Butterfly16
    • 2 years ago
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    where did you get all the numebrs?

  4. amoodarya
    • 2 years ago
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    |dw:1357845575004:dw| I dont get what you mean !

  5. Butterfly16
    • 2 years ago
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    But its for cos 15° ?

  6. amoodarya
    • 2 years ago
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    It is an unknown angle you have to make it bu known angle

  7. amoodarya
    • 2 years ago
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    you know that formula? if yeah put the numbers in it you will have answer (a)

  8. Butterfly16
    • 2 years ago
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    I think I got it. Can you help with another?

  9. klimenkov
    • 2 years ago
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    Also, you can use \(\cos^2\frac x 2=\frac{1+\cos x}2\).

  10. Butterfly16
    • 2 years ago
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    @klimenkov Can you help with this one, pelase? Write the expression as either the sine, cosine, or tangent of a single angle. \[\cos(\frac{ \pi }{ 5 }) \cos(\frac{ \pi }{ 7 }) + \sin (\frac{ \pi }{ 5}) \sin (\frac{ \pi }{ 7 })\]

  11. amoodarya
    • 2 years ago
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    as "klimenkov " says you can use that formula shuch the way i draw|dw:1357846727839:dw|

  12. amoodarya
    • 2 years ago
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    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

  13. Butterfly16
    • 2 years ago
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    so would the cos (a+b) be pi/5+pi/7?

  14. klimenkov
    • 2 years ago
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    No. It will be \(\cos(\frac\pi5-\frac\pi7)\) as @amoodarya said. Hope you can do this subtraction.

  15. amoodarya
    • 2 years ago
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    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

  16. Butterfly16
    • 2 years ago
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    \[\cos(\frac{ \pi }{ 5 }+\frac{ \pi }{ 7 })\] is 2pi/35? Can you show me how to fill in the formula? I think it'd make it easier for me.

  17. amoodarya
    • 2 years ago
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    cos (a-b)= cos a cos b+sin a sin b a=pi/5 b=pi/7

  18. Butterfly16
    • 2 years ago
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    cos (pi/5-pi/7)= cos (pi/5) cos (pi/7)+sin (pi/5) sin (pi/7) ?

  19. klimenkov
    • 2 years ago
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    Yes.

  20. Butterfly16
    • 2 years ago
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    So the answers 2pi/35?

  21. klimenkov
    • 2 years ago
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    No. The answer is \(\cos(\frac{2\pi}{35})\).

  22. Butterfly16
    • 2 years ago
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    over 25?

  23. klimenkov
    • 2 years ago
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    No. Zoom in.

  24. Butterfly16
    • 2 years ago
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    That's what I said?

  25. klimenkov
    • 2 years ago
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    You said this without cosine.

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