Solve the problem.
-The output voltage of a generator is given by $\mathrm { V } = 166 \cos \left( 2 \pi \mathrm { ft } - \frac { \pi } { 6 } \right)$. Express the voltage as the sum of a sine and a cosine function.
A) $\mathrm { V } = 83 \cos 2 \pi \mathrm { ft } + 83 \sin 2 \pi \mathrm { ft }$
B) $V = 83 \sqrt { 3 } \sin 2 \pi \mathrm { ft } + 83 \cos 2 \pi \mathrm { ft }$
C) $V = 83 \sqrt { 3 } \cos 2 \pi f \mathrm { ft } - 83 \sin 2 \pi \mathrm { ft }$
D) $\mathrm { V } = 83 \sqrt { 3 } \cos 2 \pi \mathrm { ft } + 83 \sin 2 \pi \mathrm { ft }$

Question

Quizplus · Accepted Answer

The given function can be expressed as a sum of sine and cosine functions using the cosine of a sum formula, $\cos(a - b) = \cos a \cos b + \sin a \sin b$, leading to the correct transformation.

Solve the Problem V=166cos⁡(2πft−π6)\mathrm { V } = 166 \cos \left( 2 \pi \mathrm { ft } - \frac { \pi } { 6 } \right)V=166cos(2πft−6π​)

Solve the Problem $\mathrm { V } = 166 \cos \left( 2 \pi \mathrm { ft } - \frac { \pi } { 6 } \right)$