Let theta be an angle in quadrant IV such that cos theta 78

Let theta be an angle in quadrant IV such that cos theta = 7/8. Find the exact values of csc theta and tan theta. csc theta = tan theta =

Solution

cos = 7/8

==> sin = -(1 - cos² )     (negative sign because sine function is negative in Quadrant IV)

==> sin = -(1 - (7/8)²) = -((64 - 49)/64)

==> sin = -(15/64) = -(15)/8

csc = 1/sin = 1/(-15/8) = -8/15

tan = sin/ cos = (-15/8) / (7/8)

==> tan = -(15)/7