Math

if tan theta = 3/4 and 180 degrees ≤ 0 ≤ 270 degrees determine with the aid of a complete sketch

1. sin theta
2. cos(180 +theta)
3. angle theta

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  1. By "a complete sketch" they very likely want a right-angled triangle.
    since tanØ = opposite/adjacent = 3/4 and the angle is in the third quadrant
    y = -3 and x = -4
    r^2 = 9 + 16 = 25
    r = 5

    sin Ø = -4/5

    cos(Ø + 180)
    = cosØcos180 - sinØsin180
    = (cosØ)(-1) - 0
    = - cosØ , you should know that identity
    = -(-4/5)
    = 4/5

    Ø = 180 + tan^-1 (3/4)

    = appr 216.9°

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