Answer
(a) $0.979399$
(b) $-1.905608$
(c) $1.936213$
Work Step by Step
(a) Since $78^\circ 21'=78^\circ+(\frac{21}{60})^\circ=78.35^\circ$, use a scientific calculator, we have $sin78^\circ21'=sin78.35^\circ\approx0.979399$
(b) Since $117.689^\circ$ is in quadrant II with reference angle $180^\circ-117.689^\circ=62.311^\circ$, use a scientific calculator, we have $tan117.689^\circ=-tan62.311^\circ\approx-1.905608$ (some calculators allow you to get $tan117.689^\circ$ directly)
(c) Since $sec\theta=\frac{1}{cos\theta}$, use a scientific calculator, we have $sec58.9041^\circ=\frac{1}{cos58.9041^\circ}\approx1.936213$
