## anonymous 4 years ago if x is a positive acute angle and cos x = radical 3/4, what is the exact value of sin x?

1. anonymous

|dw:1352794320204:dw|

2. 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)

3. anonymous

|dw:1352794508956:dw|

4. anonymous

i got 5/4 but thats not one of the choices. do you see where i went wrong?

5. 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

6. anonymous

Hrm. Ok. Uhhh what are all the choices?

7. anonymous

sqrt 3/5, sqrt 13/4, 3/5, 4/5

8. anonymous

it's sqrt 13/4

9. hartnn

alternative way: sin^2 x + cos^2 x = 1

10. 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.

11. anonymous

Woops for the first equation it should be sqrt3, not sqrt 13

12. anonymous

lol and it should be 13=x^2, not 13=x. I hate the equation thing.

13. anonymous

lol so what i did was correct right?

14. 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.

15. anonymous

So the final answer you got SHOULD be $\sin=\sqrt{13}/4$

16. 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?

17. 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.

18. anonymous

ughh didnt see that, thanks lol !