Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

keelyjm

  • 2 years ago

help with inverse trig functions?

  • This Question is Closed
  1. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Find the exact value of sin(arctan(2)). For full credit, explain your reasoning.

  2. AravindG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well first try to make than tan inverse inside the bracket to sin inverse so that we get sin (sin-1)

  3. AravindG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    drawing a triangle can help you do that

  4. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Drawing a triangle will help change tan-1 to sin-1?

  5. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Let arctan 2 = x so, tan x = 2 /1 since you know tan x = opposite side/adjacent side make a right angled triangle with one leg =2 and other leg = 1 |dw:1359734613467:dw| now can you find the hypotenuse ??

  6. AravindG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep :) just draw ..you will see

  7. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    once you find the hypotenuse, find sin x.

  8. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sqrt 5

  9. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    because sin(arctan(2)). = sin x

  10. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, so sin x = sin (arctan 2) =...?

  11. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sqrt5?

  12. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    thats the hypotenuse . sin ratio = opposite side / hypotenuse =... ?

  13. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh so it's 2/sqrt5

  14. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yup .

  15. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    any doubts ?

  16. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    alright and what about finding the exact real value of arccos(sqrt2/2)?

  17. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no I understand that now that you have to use a tiangle to solve it

  18. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    arccos(sqrt2/2) =x cos x = sqrt2/2 = 1/sqrt 2 for what value of angle 'x' is cos x = 1/sqrt 2 its one of the standard angle....

  19. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    also, next time please ask new question in new post...

  20. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay sorry. I am not sure how you got cos x = sqrt2/2 = 1/sqrt 2 ?

  21. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you know unit circle ? which defines standard values of sin/cos for standard angles...

  22. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i suggest you learn and remember all standard angles and values..

  23. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i know the unit circle. is that pi/4? 45 degrees?

  24. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, exactly :)

  25. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so pi/4 would be the exact real value?

  26. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\arccos(\frac{\sqrt{2}}{2})\] see if you recall an angle whose cosine is \(\frac{\sqrt{2}}{2}\)

  27. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes. pi/4 in radians 45 in degrees.

  28. keelyjm
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much!

  29. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    welcome ^_^

  30. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.