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anonymous

  • 5 years ago

Use identities (no calculators) to nd the exact value for (sin pi/4)(cos pi/2) + (cos pi/4)(sin pi/2)

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  1. anonymous
    • 5 years ago
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    this ones the hardest of them all

  2. anonymous
    • 5 years ago
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    but if you have a look at it, see what expansion it looks like

  3. anonymous
    • 5 years ago
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    and it becomes pretty easy

  4. anonymous
    • 5 years ago
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    this = sin(pi/4 + pi)??

  5. anonymous
    • 5 years ago
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    no

  6. anonymous
    • 5 years ago
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    sorry pi/2 + pi/4

  7. anonymous
    • 5 years ago
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    =sin 3/4 pi = sin 75 degrees

  8. anonymous
    • 5 years ago
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    i/m lost now!!

  9. anonymous
    • 5 years ago
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    can sin 75 degrees be written in surd form?

  10. anonymous
    • 5 years ago
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    its not 75 :|

  11. anonymous
    • 5 years ago
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    but sin75 can be written in surd form

  12. anonymous
    • 5 years ago
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    no hold om 3/4 pi = 3/4 X 180 = 135 degrees ruyght?

  13. anonymous
    • 5 years ago
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    in which case sin 135 = 1 /sqrt 2

  14. anonymous
    • 5 years ago
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    you can use sum angles expansion to find exact value of sin75 sin75 = sin(30+45) = sin30cos45+cos30sin45

  15. anonymous
    • 5 years ago
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    yes

  16. anonymous
    • 5 years ago
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    my brains not working to well today !

  17. anonymous
    • 5 years ago
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    Mathematica returns zero after entering the problem expression. The left side of the + sign is zero because Sin[Pi]= zero. Same way for the right side.

  18. watchmath
    • 5 years ago
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    It is equal to \(\sin(\frac{\pi}{4}+\frac{\pi}{2})=\sin(3\pi/4)=\sqrt{2}/2\)

  19. anonymous
    • 5 years ago
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    (Sin pi/4) was processed as Sin(pi)/4 by Mathematica.

  20. anonymous
    • 5 years ago
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    Wolfram may be incorrect but they are reporting that \[\text{Sin}\left[\frac{3 \pi }{4}\right]=\frac{1}{\sqrt{2}}\]

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