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anonymous

  • 5 years ago

Use identities (no calculators) to find the exact value for (sin 9)(sin 36)-(cos 9)(cos 36)

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  1. anonymous
    • 5 years ago
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    9+36 =?

  2. anonymous
    • 5 years ago
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    how can you play with those angles to get an angle for which there is an exact value

  3. anonymous
    • 5 years ago
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    does this equals cos 45?

  4. anonymous
    • 5 years ago
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    yes

  5. anonymous
    • 5 years ago
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    which is 1/ sqrt(2)

  6. anonymous
    • 5 years ago
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    \[\sin \theta = \cos 90 - \theta\]

  7. anonymous
    • 5 years ago
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    How do I figure out if its positive of negative

  8. anonymous
    • 5 years ago
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    sines, cosines and tangents in the first quadrant (0-90 degrees) are all positive

  9. anonymous
    • 5 years ago
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    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)

  10. anonymous
    • 5 years ago
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    this is not the formula for \[cos(a+b)\] but it is its negative.

  11. anonymous
    • 5 years ago
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    of course 9+36=36+9=45

  12. anonymous
    • 5 years ago
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    but the formula for \[cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\]

  13. anonymous
    • 5 years ago
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    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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