anonymous
  • anonymous
Use identities (no calculators) to fi nd the exact value for (sin 9)(sin 36)-(cos 9)(cos 36)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
9+36 =?
anonymous
  • anonymous
how can you play with those angles to get an angle for which there is an exact value
anonymous
  • anonymous
does this equals cos 45?

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anonymous
  • anonymous
yes
anonymous
  • anonymous
which is 1/ sqrt(2)
anonymous
  • anonymous
\[\sin \theta = \cos 90 - \theta\]
anonymous
  • anonymous
How do I figure out if its positive of negative
anonymous
  • anonymous
sines, cosines and tangents in the first quadrant (0-90 degrees) are all positive
anonymous
  • anonymous
i've just checked my maths formula book and the given expression = -cos(9 + 36) not cos (9+36) so the correct answer is -(1/sqrt2)
anonymous
  • anonymous
this is not the formula for \[cos(a+b)\] but it is its negative.
anonymous
  • anonymous
of course 9+36=36+9=45
anonymous
  • anonymous
but the formula for \[cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\]
anonymous
  • anonymous
and \[sin(a)sin(b)-cos(a)cos(b)=-(cos(a)cos(b)-sin(a)sin(b)\] that is why you had to change the sign from \[\frac{\sqrt{2}}{2}\]to \[-\frac{\sqrt{2}}{2}\]

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