Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Satsuki

  • 9 months ago

Solve the trigonometric equation on the interval [0,2π) 2cos2θ = -√(3) I did θ=5π/12 + kπ and θ=π/12 + kπ and I got { π/12 , 5π/12, 13π/12, 17π/12} as my solution set but when I plug them back in and check on my calculator they don't all equal -√3, what mistakes did I make? (Or is this right?)

  • This Question is Open
  1. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 5

    \[\cos2\theta=-\frac{ \sqrt{3} }{ 2 }\]

  2. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 5

    \[2\theta= \pi+ \cos^-1\frac{ \sqrt{3} }{ 2 } or =\pi-\cos^-1\frac{ \sqrt{3} }{ 2 }\]

  3. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 5

    two solution bcozzz cos gives negative value only in 2nd quadrent that is pi-angle or in third quadarent that is pi + angle 2 theta=pi +pi/3 .....or 2 theta= pi-pi/3 theta = (4pi/3)/2....or theta=(2pi/3)/2 theta=2pi/3......or theta=pi/3

  4. Satsuki
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If I follow correctly, then that means the solution set will only be {5π/12 , 17π/12}, correct?

  5. 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.