Pre-Calculus

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Evaluate the expression under the given conditions.? show work please!

sin(A-B); tan A=12/5, A in quadrant 3, sinB=-3sqrt(10)/10, B in quadrant 4.

  • Pre-Calculus -

    Construct 2 triangles,
    one in quad III for angle A with sides x=-5, y = -12 and r = 13
    another in quad IV for angle B with sides x = √10 , y = 3√10 and r = 10

    then sinA = -12/13, cosA = -5/13
    sinB = 3√10/10 , cosB = √10/10

    sin(A-B) = sinAcosB - cosAsinB
    = (-12/13)(√10/10) - (-5/13)(-3√10/10)
    = (-12√3 - 15√10)/130
    = -27√10/130

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