Pre Calc

posted by .

tan(x)=5 sin(x) for interval -π < x < π

A) 0, 1.571 B) -1.571, 0, 1.571 C) -1.369, 0, 1.369 D) 0, 1.369

  • Pre Calc -

    recall that tan(x) can be rewritten as
    tan (x) = sin (x) / cos (x)
    substituting:
    sin(x) / cos(x) = 5 sin(x)
    the sin(x) will be cancelled:
    1/cos(x) = 5
    cos(x) = 1/5
    solving this,
    x = +/- 1.369
    since it must be on interval -π < x < π
    x = - 1.369

  • Pre Calc -

    are we solving ????

    tanx = 5sinx
    sinx/cosx= 5sinx
    sinx = 5sinxcosx
    sinx - 5sinxcos)=0
    sinx(1 - 5cosx) = 0
    sinx = 0 or cosx = 1/5

    if sinx = 0, x = 0, π or 2π

    if cosx = 1/5, x = 1.369 or -1.369 if -π < x < π

    so for the given domain
    x = -1.369 , 0, 1.369 , which would be choice C)

  • Pre Calc -

    Thanks so much guys!!!!

  • Pre Calc -

    Did you notice that Jai missed one of the answers of
    x = 0.
    You should not cancel sinx , but rather use it as one of the factors.
    by canceling sinx , he "lost" the answer to sinx = 0

  • Pre Calc -

    oh yeah,, sorry about that. 0 is also a solution~
    thanks for correcting me, sir~ :)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Evaluate *Note - We have to find the exact value of these. That I know to do. For example sin5π/12 will be broken into sin (π/6) + (π/4) So... sin 5π/12 sin (π/6) + (π/4) sin π/6 cos π/4 + cos …
  2. Math integrals

    What is the indefinite integral of ∫ [sin (π/x)]/ x^2] dx ?
  3. Pre Calc

    evaluate the trigonometric function of the given quadrantal angle. tan 1400° cos 9π cos 13π/2 sin (-17π)
  4. Precalculus

    Use one of the identities cos(t + 2πk) = cos t or sin(t + 2πk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(19π/4) (b) sin(−19π/4) (c) cos(11π) (d) cos(53π/4) …
  5. Pre-Calc : Verify the Identity

    Verify the Identity: sin(x+π)/cos(x+3π/2) =tan^2x-sec^2x I've done: sinxcosπ+cosxsinπ / cosxcos(3π/2) - sinxsin(3π/2) sinx(-1) + cosx(0) / cosx(0)- sinx(-1) -sinx/sinx What do I do from here?
  6. Calculus

    How do I find the critical values? y= 4/x + tan(πx/8) What I did is I simplified it to y= 4x^-1 + tan(πx/8) then I took the derivative y'= -4x^-2 + (π/8)(sec(πx/8))^2 Then I simplied it y'= -4/x^2 + (π/8)(sec(πx/8))^2
  7. Math, please help

    Which of the following are trigonometric identities?
  8. Precalc/Trig

    Sorry there are quite a few problems, but I just need to know if these are correct (and if they aren't, where I went wrong): 1. Solve these equations. tanθ = -√3 θ = 2π/3 + kπ θ = 5π/3 + kπ …
  9. precalc

    Given that sec 3π/10 ≈ 17/10 and csc 3π/10 ≈ 17/14, find the following: 1. sin 3π/10 ≈ 14/17 (is this one correct) 2. csc 43π/10 ≈ 3. sec 2π/10 ≈ 4. cot -12π/10 ≈ 5. …
  10. math

    Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval square bracket0, 2π) sin 2x + 1.5 cos x = 0 a. x = 1.624, 1.932, 5.776, 5.997 b. x = 1.055, 3.785, 4.652, 5.721 …

More Similar Questions