Trig

posted by .

Determine the roots of the function f(x)=-2cos(3x)-1. Can you please show all the work so it is easier to understand, thank you!!

  • Trig -

    set 2cos(3x) - 1 = 0
    2cos(3x) = 1
    cos 3x = 1/2
    I will use degrees, we can always switch to radians later
    3x = 60° or 3x = 300° by the CAST rule
    x = 20° or x = 100°

    the period of cos 3x = 360/3 or 120°
    so by adding/subtracting 120° to any of our answers we can produce as many new answers as we want,
    so for 0 ≤ x ≤ 360°
    x = 20°, 140°,100° , 220° , 260°, 340°

    or in radians
    x = π/9, 7π/9, 5π/9, 11π/9 , 13π/9, 17π/9

  • Trig -

    Ok so how did you get x to equal 20, 140,100........
    And I also don't get where 3x=60 or 100 came from, can you please explain these parts by showing the math? Thank you

  • Trig -

    I knew, or my calculator told me, that
    cos 60° = 1/2 or cos 300° = 1/2
    so 3x had to be 60° or 3x had to be 300°

    well if 3x = 60 , what is x? (divide both sides by 3)
    same for 3x = 300
    x = 100

    (on your calc.
    enter
    2nd
    cos
    .5
    =

    you should get 60 )

  • Trig -

    Srry I keep asking questions, but I noticed that you left out the negative sign on the 2 when you set the equation to zero, was that a mistake or were you suppose to do it like that?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trigonometry

    Need help solving problems using the Trigonometric Identities: 8cos^4 thet=cos4theta+4cos2theta+3 I am a bit unsure how to solve it. I am aware that the first step I must take is to simplify the problem and then use the Product to …
  2. trig

    The average depth of water at the end of a dock is 6 ft. This varies 2 ft in both directions with the ride. Suppose there is a high tide at 4 am. If the tide goes from low to high every 6 hours, write a cosine function describing the …
  3. Precalculus

    "Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary …
  4. maths

    q1) 2cos2x is f(x) -square root3 is g(x) solve f(x)-g(x)=0 to get points of intersection in x is between 0 and 180degrees q2) a) write the equation cos2x + 8cosx+9=0 in terms of cosx and show that for cosx it has equal roots q2b) show …
  5. Math - Graphing Logarithms function

    Graph the function below. Determine the domain, range, and vertical asymptote. Please show all of your work. f(x) = log2(x-4)
  6. Math 3

    Find the inverse of the function f(x) = 5 – e^(x-1). Determine the domain, range, and asymptotes of the function and its inverse function. Please show all of your work.
  7. College Algebra

    Find the inverse of the function below. Graph the function below and the inverse function. Determine the domain, range, and asymptotes of the function below and the inverse function. Please show all of your work. Show both graphs. …
  8. trig

    I don't understand this. can you please tell how you got each answer?
  9. MATH PLEASE SHOW WORK

    Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND …
  10. calc

    determine the intersection pints of the graphs of the equations y=x^3-4x y=-x-2 I dont understand this please show all work.

More Similar Questions