anonymous
  • anonymous
if x is a positive acute angle and cos x = radical 3/4, what is the exact value of sin x?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1352794320204:dw|
anonymous
  • anonymous
Mk so cos is adjacent over hypotenuse, |dw:1352794400088:dw|, now you just have to use Pythagorean theorem to solve for the last side. Sin is opposite over hypotenuse, so you're going to take the value you found from Pythagorean theorem and put that over 4 (the hypotenuse value)
anonymous
  • anonymous
|dw:1352794508956:dw|

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anonymous
  • anonymous
i got 5/4 but thats not one of the choices. do you see where i went wrong?
anonymous
  • anonymous
one of the choices are 4/5 but im not sure, because i found the leg using the pythagorean theorem and got b(squared) = 25 which makes b= 5 and then over the hypotenuse which gave me 5/4
anonymous
  • anonymous
Hrm. Ok. Uhhh what are all the choices?
anonymous
  • anonymous
sqrt 3/5, sqrt 13/4, 3/5, 4/5
anonymous
  • anonymous
it's sqrt 13/4
hartnn
  • hartnn
alternative way: sin^2 x + cos^2 x = 1
anonymous
  • anonymous
You shouldn't be getting 5 for the last leg, because Pyth, should give you \[4^{2}=\sqrt{13}^{2}+x ^{2}\], which then becomes \[16=3+x ^{2}\], then \[13=x\], so x = sqrt 13.
anonymous
  • anonymous
Woops for the first equation it should be sqrt3, not sqrt 13
anonymous
  • anonymous
lol and it should be 13=x^2, not 13=x. I hate the equation thing.
anonymous
  • anonymous
lol so what i did was correct right?
anonymous
  • anonymous
Uhh you did the right thing, you just did it wrong. You go the wrong answer from Pyth. Theorem by yeah you're supposed to use that and then put it over 4.
anonymous
  • anonymous
So the final answer you got SHOULD be \[\sin=\sqrt{13}/4\]
anonymous
  • anonymous
i have a (squared) and c(squared) which means im looking for b (squared) i solved and got 9 +b(squared)=16, subtracted on both sides by 9 and got b2 = 7, not 5 my mistake, where did u get 13 from?
anonymous
  • anonymous
Aiiight. The thing is, your side length isn't 3, it's the sqrt of 3. So sqrt of 3 squared is 3. So then you take 16, which is 4 sqared, and subtract 3 from that, giving you 13. Then you end up with 13 = x squared. Take the square root of both sides, and you get square root of 13. Put that over 4 (hypotenuse) for your final answer.
anonymous
  • anonymous
ughh didnt see that, thanks lol !

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