trigonometry

solve the equation: 4 tan^2 x + 12 sec x +1 =0, for 0 degrees is less than or equal to x is less than or equal to 360 degrees.

  1. 👍
  2. 👎
  3. 👁
  1. 4 tan^2 x + 12 sec x +1 =0
    4sin^2 x/cos^2 x + 12/cosx + 1 = 0
    times cos^2 x
    4sin^2x + 12cosx + cos^2x = 0
    4(1-cos^2 x) + 12cosx + cos^2 x = 0
    -3cos^2 x + 12cosx + 4 = 0
    3cos^2 x - 12cosx - 4 = 0
    cosx = (12 ± √192)/6
    = 4.309.. which is not possible, or cosx = -.3094..

    so x must be in quads II or III
    x = 180-71.977° or x = 180+71.977
    x = 108.02° or 251.98°

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Prove that the equation Is an identity. Sec^4x - Tan^4x = Sec^2x + Tan^2x

  2. Pre-Cal

    1)tan 5 degrees + tan 25 degrees / 1 tan 5 degrees tan 25 degrees = sqrt 3 / 3 Am I correct? 2) Complete the identity tan^2Q - 3sinQtanQsecQ = -2tan^2Q Correct?

  3. inverse trig functions

    evaluate the following expressions: tan(sec^-1(5/3)) tan(sec^-1(25/7)) cot(csc^-1(5/3)) i know the answers.. i jus don't know how to solve them =( PLEASE help me I assume your sec^-1 notation denot4es the arcsecant function, etc.

  4. trigonometry

    Find all the angles between 0 degrees and 360 degrees which satisfy the equations a. 8 cos x sin x = sin x b. 5 tan^2 y + 5 tan y = 2 sec^2 y.

  1. Trigonometry

    How do you verify the equation is an identity? Tan^2x-tan^2y=sec^2x-sec^2y and, how do you factor and simplify, cscx(sin^2x+cos^2xtanx)/sinx+cosx

  2. Math

    Solve:(sec 35 degrees) (csc 55 degrees) - (tan 35 degrees) (cot 55 degrees)

  3. trig

    Solve the equation 2 tan C - 3 = 3 tan C-4 algebraically for all values of C in the interval 0 degrees

  4. Trig

    Two observers 1 km apart spot an airplane. The angles of elevation of the airplane from the two observers are 22 degrees 50 minutes and 24 degrees 40 minutes. If the observers and the airplane are in the some vertical plnae,

  1. Trigonometry

    1. Find the exact value of the following (Think identity) Cos(2 Arccos(5/13)) 2. Solve the following equation for 0° ≤ Θ < 360° Sec(Θ)= tan(Θ) + cos(Θ)

  2. Trig

    Solve the equation on the interval 0 less than or equal 0 < 2pi. 1. sec 30/2 = -2 2. cos(20 - pi/2) = -1 3. tan(0/2 + pi/3) = 1

  3. Math

    Determine each tangent ratio to four decimal places using a calculator. A) tan 74 degrees B) tan 45 degrees C) tan 60 degrees D) tan 89 degrees How do I figure this out !?

  4. trig

    solve equation for the exact solutions if possible put answer in degrees. 2tanx/3-tan^2x=1

You can view more similar questions or ask a new question.