anonymous
  • anonymous
find cos(sin-1(3/5))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Draw a right angled triangle.
anonymous
  • anonymous
done
anonymous
  • anonymous
can't you just plug it in your calculator? find the inside function and then put that value into the cos equation?

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anonymous
  • anonymous
no calculator allowed
anonymous
  • anonymous
Yes, you can put it in you calculator... and learn nothing.
anonymous
  • anonymous
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).
anonymous
  • anonymous
x = sin^-1(3/5), by the way
amistre64
  • amistre64
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
amistre64
  • amistre64
cos-1(cos(a)) = 4/5
anonymous
  • anonymous
cos^-1(cos(a)) = a, actually ;)
amistre64
  • amistre64
hmm..... thats right. lol
amistre64
  • amistre64
there aint no simple angles from trig to give you a cosine of 4/5; or a sin of 3/5 :)
anonymous
  • anonymous
the answer is 4/5 right?
anonymous
  • anonymous
Yes (but my method was better :p)
anonymous
  • anonymous
what would cos(sin(3/5)) be?
anonymous
  • anonymous
That would be .. a lot harder (if neither are ^-1)
anonymous
  • anonymous
sorry cos-1(sin(3/5))
anonymous
  • anonymous
woops
anonymous
  • anonymous
\[\cos^{-1}\left[\sin\left(\frac{3}{5}\right)\right] = x \iff \sin\left(\frac{3}{5}\right) = \cos(x)\]
anonymous
  • anonymous
Are you working in radians or degrees?
anonymous
  • anonymous
radians i assume. the problem calls for the exact value
anonymous
  • anonymous
By definition: \[\sin(\alpha) = \cos\left(\frac{\pi}{2}-\alpha\right) \text{ and } \cos(\alpha) = \sin\left(\frac{\pi}{2}-\alpha\right) \]
anonymous
  • anonymous
So if sin(3/5) = cos(x), then x = ....
anonymous
  • anonymous
3/5 ?
anonymous
  • anonymous
im sorry those formulas are in my book and i can't understand them.
anonymous
  • anonymous
They aren't in your book, do you mean?
anonymous
  • anonymous
are. i have example problems i just wanted it broken down.
anonymous
  • anonymous
i have to go. thanks for the bit of help though! sorry i couldn't do more with it
anonymous
  • anonymous
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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