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Find the exact value of the trigonometric function given that

sin u = 5/13 and cos = -3/5

1) sin(u-v)

My teacher said to make two right triangles and then find the missing parts by the pyth theorem.

For the 5/13 triangle I got 12 and the other triangle I got 4. I do not know what to do now.

  • Math -

    so the angle u could be in quadrant I inside a 5:12:13 triangle, with 13 as the hypotenuse,
    so cos u = 12/13

    angle v could be in quadrants II or III and are inside the 3:4:5 triangle , with 5 the hypotenuse, so
    sin v = 4/5
    draw the triangle in quadrant II with those dimensions

    You must by now have learned that
    sin(A-B) = sinAcosB - cosAsinB

    then sin(u-v) = sinucosv - cosusinv
    = (5/13)(-3/5) - (12/13)(4/5) = -63/65

  • Math -

    Thank You

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