Use the cofunction identities to find an angle that makes the statement true.
-The output voltage of a generator is given by $\mathrm { V } = 158 \cos \left( 2 \pi \mathrm { ft } - \frac { \pi } { 6 } \right)$. Express the voltage as the sum of a sine and a cosine function.
A) $V = 79 \sqrt { 3 } \cos 2 \pi \mathrm { ft } + 79 \sin 2 \pi \mathrm { ft }$
B) $V = 79 \sqrt { 3 } \sin 2 \pi \mathrm { ft } + 79 \cos 2 \pi \mathrm { ft }$
C) $V = 79 \cos 2 \pi \mathrm { ft } + 79 \sin 2 \pi \mathrm { ft }$
D) $V = 79 \sqrt { 3 } \cos 2 \pi \mathrm { ft } - 79 \sin 2 \pi \mathrm { ft }$

Question

Quizplus · Accepted Answer

Using the cosine sum formula, $\cos(a - b) = \cos a \cos b + \sin a \sin b$, with $a = 2\pi ft$ and $b = \frac{\pi}{6}$, we get $V = 158(\cos(2\pi ft)\cos(\frac{\pi}{6}) + \sin(2\pi ft)\sin(\frac{\pi}{6}))$. Since $\cos(\frac{\pi}{6}) = \sqrt{3}/2$ and $\sin(\frac{\pi}{6}) = 1/2$, the expression simplifies to $V = 79\sqrt{3}\cos(2\pi ft) + 79\sin(2\pi ft)$.

Use the Cofunction Identities to Find an Angle That Makes V=158cos⁡(2πft−π6)\mathrm { V } = 158 \cos \left( 2 \pi \mathrm { ft } - \frac { \pi } { 6 } \right)V=158cos(2πft−6π​)

Use the Cofunction Identities to Find an Angle That Makes $\mathrm { V } = 158 \cos \left( 2 \pi \mathrm { ft } - \frac { \pi } { 6 } \right)$