Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Trending News

Promoted
Dylan
Lv 6
Dylan asked in Science & MathematicsMathematics · 5 years ago

If x=3sin(theta) What is -cos(theta) in terms of x using the method of triangles Answer is -sqrt(9-x^2)?

2 Answers

Relevance
  • Keith A
    Lv 6
    5 years ago
    Favorite Answer

    Triangles:

    Take 3 as the hypotenuse of a right triangle,

    and x opposite the angle θ -- assuming θ is acute.

    Then the third side - adjacent to θ, is √(9 - x²)

    So cos θ = √(9 - x²) / 3 ,

    -cos θ = -√(9 - x²) / 3 .

  • Wayne DeguMan
    Lv 7
    5 years ago

    If x = 3sinθ then,

    sinθ = x/3

    Now, sin²θ + cos²θ = 1

    i.e. (x/3)² + cos²θ = 1

    => cos²θ = 1 - (x²/9)

    => 9cos²θ = 9 - x²

    so, cos²θ = (9 - x²)/9

    => cosθ = ±√(9 - x²)/3

    Hence, -cosθ = -√(9 - x²)/3

    :)>

Still have questions? Get your answers by asking now.