Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

lilsis76 Group Title

suppose sin theta = 1/5 and 0<theat< pi/2 compute cos theta and compute sin 2theta... i have these formulas given but i dont know what to do with them. let me draw them

  • one year ago
  • one year ago

  • This Question is Closed
  1. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1350681532092:dw|

    • one year ago
  2. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i have these formulas given... The expressions you posted are specific examples, not formulas. To answer this question suppose sin x = 1/5 and 0<x< pi/2 (Let me use x, it's easier to type than theta) First, recall the definition of sin: opposite over hypotenuse. 2nd, it is helpful to draw a graph. |dw:1350682184808:dw|

    • one year ago
  3. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    they tell us x is between 0 and pi/2 (90º) so we know x is in the first quadrant. the cos x is adjacent over hypotenuse. we know the hypotenuse (it's 5) use pythagorean theorem to find the bottom leg of the right triangle (that will be the adjacent side we need for the cos) can you do that?

    • one year ago
  4. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes let me try it on a paper.

    • one year ago
  5. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    a= sqrt 24 -> i can reduce giving me a=sqrt 4 sqrt 6 a= 2sqrt6

    • one year ago
  6. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, use a's value to find \[ \cos(x)= \frac{2\sqrt{6}}{5}\]

    • one year ago
  7. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1350682709676:dw|

    • one year ago
  8. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry about that, this thing is being slow, this openstudy site

    • one year ago
  9. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    to find compute sin 2x I remember sin(a+b)= sin(a)cos(b)+cos(a)sin(b) if a and b are the same=x, we can write this as sin(x+x) = sin(x) cos(x) + cos(x) sin(x) sin(2x)= 2 sin(x) cos(x) so replace sin(x) with 1/5 and cos(x) with 2sqrt(6)/5 in that formula and simplify to get sin(2x)

    • one year ago
  10. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    being slow Yes, sometimes it acts up. Some days are better than others.

    • one year ago
  11. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay ill try to find the first one, but how did you get \[2\sqrt{6} / 5 ? <--- how did u get the 5?\]

    • one year ago
  12. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    the cos x is adjacent over hypotenuse

    • one year ago
  13. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    how did u get the 5? haha sorry i cant read the other writting either. and i did sin 2x= sin 2(1/5) - that would make it sin 2/5 right?

    • one year ago
  14. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay i see the cos =5 now. is 2/5 right?

    • one year ago
  15. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    no. it is not the simple (otherwise it would not be math) first, what do you have for sin(x) and cos(x)?

    • one year ago
  16. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sin x is opp/hyp= 1/5 cos x is adj/hyp= 2sqrt{6}/5

    • one year ago
  17. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, that is good. I repeat my post from above to find compute sin 2x I remember sin(a+b)= sin(a)cos(b)+cos(a)sin(b) if a and b are the same=x, we can write this as sin(x+x) = sin(x) cos(x) + cos(x) sin(x) sin(2x)= 2 sin(x) cos(x) so replace sin(x) with 1/5 and cos(x) with 2sqrt(6)/5 in that formula and simplify to get sin(2x)

    • one year ago
  18. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    in the sin(a+b)= sin(a)cos(b)+cos(a)sin(b)? like sin( 1/5 + 2sqrt6/5) = sin 1/5 cos 2sqrt6/5 + cos 1/5 sin 2sqrt6/5

    • one year ago
  19. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    no. don't get confused. I was showing that the "sum of angles" formula simplifies to sin(2x)= 2 sin(x) cos(x) For example, if x were 30º, you could use this formula to find the sin(60º) sin(60)= sin(2*30)= 2 sin(30) cos(30) in this case, you are asked to find the sin(2x). You know sin(x) and cos(x). Can you find sin(2x)?

    • one year ago
  20. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    sin x is opp/hyp= 1/5 cos x is adj/hyp= 2sqrt{6}/5 replace sin(x) with 1/5 replace cos(x) with 2sqrt{6}/5 in the formula sin(2x)= 2 sin(x) cos(x)

    • one year ago
  21. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay let me try it. i am trying to find it on my paper

    • one year ago
  22. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay i got this then

    • one year ago
  23. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sin 2x = 2 sin 1/5 cos 2sqrt 6 / 5

    • one year ago
  24. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    be careful x is not 1/5 sin(x) is 1/5 try again.

    • one year ago
  25. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay

    • one year ago
  26. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sin 2x = 2sin 1/5 cos x

    • one year ago
  27. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thats all im understanding

    • one year ago
  28. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    when we say sin x =1/5 and then write, for example cos(x) sin(x) we can replace sin(x) with 1/5 (that is what = means) so cos(x) sin(x) could be written as cos(x) * 1/5 can you use that idea in sin(2x)= 2 sin(x) cos(x) when sin x= 1/5 cos x= 2sqrt{6}/5

    • one year ago
  29. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    in other words, replace sin x with 1/5 and replace cos(x) with 2sqrt(6)/5

    • one year ago
  30. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    into the formula you gave me? the...sin(2x)= 2 sin(x) cos(x) ? what is that equation for also?

    • one year ago
  31. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, in the formula sin(2x)= 2 sin(x) cos(x) I'll post a video that explains this, so you can watch it when you have time.

    • one year ago
  32. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay, thank you

    • one year ago
  33. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    like this: 2(1/5) = 2(1/5)(2sqrt6 / 5) ?

    • one year ago
  34. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    HEYY?! i just realized, did we solve the compute cos theta? was that the 2sqrt6 / 5?

    • one year ago
  35. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    closer. we know sin(x) and cos(x). but we do not know sin(2x) we start with sin(2x)= 2 sin(x) cos(x) replace sin(x) with 1/5 sin(2x)= 2* 1/5 * cos(x) replace cos(x) with 2sqrt6/5 sin(2x)= 2* 1/5 * 2sqrt6/5 notice that sin(2x) is not 2*1/5

    • one year ago
  36. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hmmm....okay

    • one year ago
  37. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    will the 2 (1/5) = 2/5? or is that wrong?

    • one year ago
  38. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i ddont know how to mult. fractions.

    • one year ago
  39. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes 2*1/5 is 2/5 the answer is \[ \sin(2\theta)= \frac{4\sqrt{6}}{25} \] (I used theta again just to match the problem)

    • one year ago
  40. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is the first video on trig http://www.khanacademy.org/math/trigonometry/v/basic-trigonometry

    • one year ago
  41. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh....okay, thank you ill watch the video. but one quesiton. why dont we multiply the sqrt by the 2 also?

    • one year ago
  42. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is a list of videos on fractions http://www.khanacademy.org/math/arithmetic/fractions I would watch the first few just to see if they make sense. Later on, if you run into a problem, go to this site and search for a video that explains it.

    • one year ago
  43. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay. thank you so much. imma watch a few of these then get back to the homework.

    • one year ago
  44. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \sin(2x)= 2\cdot \frac{1}{5} \cdot \frac{ 2\sqrt{6}}{5} \] to multiply fractions you multiply top*top and bottom*bottom (whole numbers are "tops") \[ \sin(2x)= \frac{2\cdot 1 \cdot 2\sqrt{6}}{5\cdot 5} \] that simplifies to \[ \sin(2x)= \frac{4\sqrt{6}}{25} \]

    • one year ago
  45. lilsis76 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh...okay now i see it, dang lol i never saw it like that before. well thank you I shall watch the videos and ill be back later

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.