sinӨ, if cosӨ=2/5 and tan Ө<0 evaluate?

sinӨ, if cosӨ=2/5 and tan Ө<0 how do i work this out?

6 Answers

Relevance
  • Anonymous
    9 years ago
    Favorite Answer

    From the cosine information we have a triangle whose X leg is 2 and whose hypotenuse is 5. The length of the Y leg is therefore sqrt(25-4) = sqrt(21).

    Since the tangent is negative we know that the angle is in quadrant IV and the sine must also be negative. Hence the sine of the angle is -sqrt(21)/5

  • Anonymous
    9 years ago

    use

    sin^2 + cos^2 = 1

  • 9 years ago

    Draw a right triangle representing cosӨ = 2/5 . . . (adjacent = 2 / hypot = 5)

    Use pythag to find 'opposite' . . .

    Find sinӨ (opposite / hypot).

  • s k
    Lv 7
    9 years ago

    sin(x)^2 + cos(x)^2 = 1

    So sin(x) = ±√(1 - cos(x)^2)

    = ±√(1 - 4/25)

    = ±√(21/25)

    = ±√(21)/5

    As tan(x) < 0 and cos(x) > 0, we must have sin(x) < 0.

    So sin(x) = -√(21)/5.

  • How do you think about the answers? You can sign in to vote the answer.
  • Anonymous
    9 years ago

    sinӨ^2 + cosӨ^2=1

    sinӨ^2 + 4/25=1

    sinӨ^2=21/25

    sinӨ= sqrt(21)/5

    sinӨ= -4.582/5

    sinӨ= -0.9165

  • 9 years ago

    use trig identities.

Still have questions? Get your answers by asking now.