pre-calculus

posted by .

solve cos 2x=secx for 0(<=)x<2pi using trigonometric identities.

  • pre-calculus -

    Since cos(2x) = 1 at x = 0,pi,2pi,3pi,...
    sec(x) = 1 at 0,2pi,4pi,6pi,...

    They meet at even multiples of pi.

    cos never gets above 1, sec never gets below 1.

    On your interval, x=0 is the only solution

    Analytically,

    cos 2x = sec x
    2cos^2 x - 1 = 1/cosx
    2 cos^3 x - cos x - 1 = 0

    cosx = 1 is the only real solution.
    so, x=0

  • pre-calculus -

    cos(2theta)= 120/169; 2theta in QIV

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calc

    Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= tanx + secx My work so far: (sinx/cosx + 1/cosx + cosx/cosx)/(sinx/cos x - 1/cosx + cosx/cosx)= tanx + cosx (just working on the left side) ((sinx + 1 - cosx)/cosx)/((sinx …
  2. Simplifying with Trigonometry Identities

    Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each other. …
  3. Pre-Calculus

    Find the solutions for sec^2x+secx=2 that fit into the interval [0, 2pi] I figured out that pi/3 (after factoring and switching things around) was a solution, but then I got stuck on cos x = 1/3.
  4. Trig

    How do you express these problems as single trigonometric function values or as single numbers, using identities?
  5. Trig

    How do you express these problems as single trigonometric function values or as single numbers, using identities?
  6. Pre-Calc/Math

    Use factoring, the quadratic formula, or identities to solve cos(x)+1=sin^(2)x. Find all solutions on the interval [0, 2pi)
  7. trigonometric identities

    Prove the following trigonometric identities 1. tanx = sinx + sin^2x/cosx(1+sinx) 2. cos^3+(cosx)(sin^2x) = 1/secx
  8. Pre Calculus

    (secx)/(tanx)+(cscx)/(cotx)=secx+cscx Please help me verify this trigonometric identity.
  9. Pre Calculus

    (cotx)(cscx)+secx=(csc^2x)(secx) Please help to verify this trigonometric identity.
  10. Pre-calculus

    Prove the following identities. 1. 1+cosx/1-cosx = secx + 1/secx -1 2. (tanx + cotx)^2=sec^2x csc^2x 3. cos(x+y) cos(x-y)= cos^2x - sin^2y

More Similar Questions