Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

BecomeMyFan=D

  • 3 years ago

cos(3x) +0.5 = 0 I wan to understand how to solve it.

  • This Question is Closed
  1. BecomeMyFan=D
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    anyone?

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

    x = .6981317008 this is the answer btw i know it, but i dont know how to get to it

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

    Okay, you can bring the 0.5 to the right hand side and you're left with cos(3x) = -0.5. You know, or should be familiar with the fact that the arc-cosine of 0.5 is 60 degrees, or pi/3 radians. So, because the value is negative, it's in the second quadrant and you can say that it's 120 degrees, or 2*pi/3 radians. Now, you're left with 3x = 2*pi/3. Divide by 3, and see the values that come out, and you should get about 0.69813... radians.

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

    I assume 0 < x < 2pi cos(3x)=-(1/2) since we know that cos(pi/3) = 1/2 and cosine is negative in the 2nd and 3rd quadrants, we have cos(3x) = cos(2pi/3) or cos (4pi/3) or cos(2pi + 2pi/3) or cos(2pi + 4pi/3) or cos(4pi + 2pi/3) or cos(4pi + 4pi/3) = cos(2pi/3) or cos(4pi/3) or cos(8pi/3) or cos(10pi/3) or cos(14pi/3) or cos(16pi/3) Thus 3x = 2pi/3 or 4pi/3 or 8pi/3 or 20pi/3 or 14pi/3 or 16pi/3. This gives your values x between 0 and 2pi

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

    \[\cos(3x)=-0.5\] so 3x is either in the 2nd or 3rd quadrant, \[3x=2\pi/3+2n \pi\] or \[3x=4\pi/3+2n \pi, n=0,1,2,...\]

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

    first of all let's write down the equation in terms of cos ^_^ and you'll get : \[\cos(3x) = -0.5\] now you want to find x here, if you've noticed 3x acts as the angle in this question, so simply imagine it as theta and find the angle by doing the following: \[3x = \cos^{-1} -0.5\] \[ x = [\cos^{-1} (-0.5)]/3 = 2\pi/9 = 40\] Correct me if I'm wrong :)

  7. amistre64
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cos(3x) = -1/2 ; the definition of cosine consists of parts of a triangle. It will be the "leg" that is right next to it; divided by the slanted (hypotenuse); in this case, its leg=1 and slant=2 leg^2 + (opposite leg)^2 = slanted^2 -1^2 + y^2 = 2^2 1 + y^2 = 4 y^2 = 3 y=sqrt(3) or y=-sqrt(3) since the leg is (-1) we take that to be the Q2. as it turns out; 120 degrees has a cosine of -1/2 in Q2.... gotta go....

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

    I think he wanted to solve for x, right? ._.

  9. amistre64
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3x = 120 x=120/3 x=40

  10. amistre64
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    180+60 = 240 3x = 240 as well 3x=240 x=240/3 x=80...

  11. amistre64
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    figure out which one = .69813.... lol.... neither one :)

  12. 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.