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anonymous

  • 5 years ago

find cos(sin-1(3/5))

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  1. anonymous
    • 5 years ago
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    Draw a right angled triangle.

  2. anonymous
    • 5 years ago
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    done

  3. anonymous
    • 5 years ago
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    can't you just plug it in your calculator? find the inside function and then put that value into the cos equation?

  4. anonymous
    • 5 years ago
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    no calculator allowed

  5. anonymous
    • 5 years ago
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    Yes, you can put it in you calculator... and learn nothing.

  6. anonymous
    • 5 years ago
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    OK so a triangle has an angle (x) - if sin of this angle is 3/5, then one side of the triangle is 3, and the other 5 (by definition). Use pythagoras to work out the other side, and then cos (by definition).

  7. anonymous
    • 5 years ago
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    x = sin^-1(3/5), by the way

  8. amistre64
    • 5 years ago
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    sin(a) = 3/5 sin^2 + cos^2 = 1 (3/5)^2 + cos^2 = 1 cos^2 = 1 - 9/25 cos^2 = 16/25 cos(a) = 4/5

  9. amistre64
    • 5 years ago
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    cos-1(cos(a)) = 4/5

  10. anonymous
    • 5 years ago
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    cos^-1(cos(a)) = a, actually ;)

  11. amistre64
    • 5 years ago
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    hmm..... thats right. lol

  12. amistre64
    • 5 years ago
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    there aint no simple angles from trig to give you a cosine of 4/5; or a sin of 3/5 :)

  13. anonymous
    • 5 years ago
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    the answer is 4/5 right?

  14. anonymous
    • 5 years ago
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    Yes (but my method was better :p)

  15. anonymous
    • 5 years ago
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    what would cos(sin(3/5)) be?

  16. anonymous
    • 5 years ago
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    That would be .. a lot harder (if neither are ^-1)

  17. anonymous
    • 5 years ago
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    sorry cos-1(sin(3/5))

  18. anonymous
    • 5 years ago
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    woops

  19. anonymous
    • 5 years ago
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    \[\cos^{-1}\left[\sin\left(\frac{3}{5}\right)\right] = x \iff \sin\left(\frac{3}{5}\right) = \cos(x)\]

  20. anonymous
    • 5 years ago
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    Are you working in radians or degrees?

  21. anonymous
    • 5 years ago
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    radians i assume. the problem calls for the exact value

  22. anonymous
    • 5 years ago
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    By definition: \[\sin(\alpha) = \cos\left(\frac{\pi}{2}-\alpha\right) \text{ and } \cos(\alpha) = \sin\left(\frac{\pi}{2}-\alpha\right) \]

  23. anonymous
    • 5 years ago
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    So if sin(3/5) = cos(x), then x = ....

  24. anonymous
    • 5 years ago
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    3/5 ?

  25. anonymous
    • 5 years ago
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    im sorry those formulas are in my book and i can't understand them.

  26. anonymous
    • 5 years ago
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    They aren't in your book, do you mean?

  27. anonymous
    • 5 years ago
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    are. i have example problems i just wanted it broken down.

  28. anonymous
    • 5 years ago
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    i have to go. thanks for the bit of help though! sorry i couldn't do more with it

  29. anonymous
    • 5 years ago
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    Oh, OK. Well, they work because cos is just a translation of sin, by pi/2. The answer is x = pi/2 - 3/5, from the formulae

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