Solve Apps: Trigonometric Equations
-The output voltage for an $\mathrm { AC }$ generator is approximated by $\mathrm { v } = 156 \cos \left( 120 \pi \mathrm { t } - \frac { \pi } { 3 } \right)$. Find the smallest positive value of $t$ for which the output is 125 volts.
A) $0.0045$ second
B) $0.0035$ second
C) $0.0090$ second
D) $0.0100$ second

Question

Quizplus · Accepted Answer

Explanation:To find the smallest positive value of $t$ for which the output is 125 volts, we need to solve the equation $156 \cos \left( 120 \pi \mathrm { t } - \frac { \pi } { 3 } \right) = 125$. Dividing both sides by 156, we get $\cos \left( 120 \pi \mathrm { t } - \frac { \pi } { 3 } \right) = \frac { 125 } { 156 } \approx 0.8013$. Using a calculator, we find that the smallest positive value of $t$ that satisfies this equation is approximately 0.0045 seconds.

Solve Apps: Trigonometric Equations -The Output Voltage for An AC\mathrm { AC }AC

Solve Apps: Trigonometric Equations
-The Output Voltage for An $\mathrm { AC }$