Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

CEBS95

  • 2 years ago

tan^2(60) + 4cos^2(45) - 9tan^2(30) - 8sin^2(30) The answer is zero but why!? i need step by step solution please

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

    why can't you just plug the whole thing into your calculator?

  2. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because in the exam they already give you the answer, you have to do the procedure

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

    tan60 = \(\sqrt{3}\) cos45 = \(\frac{1}{\sqrt2}\) tan30 = \(\frac{1}{\sqrt3}\) sin30 = 1/2 These are all special angles and you should remember them.

  4. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i know them but i just continue to get 6 instead of 0

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

    I'm getting zero just fine though. note the squares.

  6. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    tan^2(60) = 3 ? 4cos^2(45) = 4 ?

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

    4cos^2(45) = 4 (1/2) = ...?

  8. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    my math base is not good, that's the reason i wrote step by step solution

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

    \[cos45 =\frac{1}{\sqrt2}\]\[cos^245 =(\frac{1}{\sqrt2})^2 = \frac{1}{2}\]\[4cos45 =4(\frac{1}{2}) = ...?\]

  10. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4 (1/2) = 2

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

    Yes.

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

    \[\frac{ \sin ^{2} (60)}{ \cos ^{2}(60)}+4\cos ^{2}(45)-9\frac{ \sin ^{2}(30) }{ \cos ^{2}(30) }-8\sin ^{2}(30)\]

  13. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so, tan^2(60) = 3

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

    tan^2(60) = 3 <- Yes

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

    |dw:1355048071288:dw|

  16. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i found in my book that cos 45 = \[\frac{ \sqrt{2} }{ 2}\]

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

    \[\frac{1}{\sqrt2}=\frac{1}{\sqrt2}\times \frac{\sqrt2}{\sqrt2}=\frac{\sqrt2}{\sqrt2^2} = \frac{\sqrt2}{2}\] Just rationalization.

  18. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    9tan^2(30) = \[\tan( 30) = \frac{ \sqrt{3} }{ 3 } ; \tan ^{2}(30) = 3/9 = 1/3 \]

  19. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    times 9 = 3 right?

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

    Yes.

  21. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    8 sin ^2 (30) = 4 ?

  22. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no, i think it 8

  23. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    9tan^2(30) - 8sin^2(30) = 3 - 8 = -5, at the end that will give me 5- (-5) that equals 10

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

    8 sin ^2 (30) = 8 (1/2)^2 = 8 (1/4) = ...

  25. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2

  26. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    still, 3-2 = 1, 5-1 = 4

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

    |dw:1355049445375:dw| look at this one to see how i get 0

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

    tan^2(60) + 4cos^2(45) - 9tan^2(30) - 8sin^2(30) tan^2(60) = \(\sqrt3^2\) = ... 4cos^2(45) = 4\((\frac{1}{\sqrt2})^2\) = 4(1/2) = ... - 9tan^2(30) = -9 \((\frac{1}{\sqrt3})^2\) = -9 (1/3) = ... - 8sin^2(30) = -8 (1/2)^2 = -8 (1/4) = ... Sum up the four answers.

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

    |dw:1355049643294:dw|

  30. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    zero! nice thanks calisto

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

    You're welcome :)

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

    | 30 | 45 | 60 ------------------------------------ sin | \(\frac{1}{2}\) | \(\frac{1}{\sqrt2} /\frac{\sqrt2}{2} \) | \(\frac{\sqrt3}{2}\) ------------------------------------ cos | \(\frac{\sqrt3}{2}\) | \(\frac{1}{\sqrt2} /\frac{\sqrt2}{2} \) | \(\frac{1}{2}\) ------------------------------------ tan | \(\frac{1}{\sqrt3} /\frac{\sqrt3}{3} \) | 1 | \(\sqrt{3}\)

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

    Memorize the table..

  34. CEBS95
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, with practice i will memorise the terms

  35. 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.