Question

The voltage of the alternating current coming through an electrical outlet can be modeled by the function V(t) = 167 sin(110πt), where t is measured in seconds and V in volts. Find all times at which the voltage is at its maximum. (Let k be any integer.

Answer 1

Answer:

$t = \frac{(4k + 1) }{220 }$ for k =0, 1,2,3............

Step-by-step explanation:

From the function $V(t) = 167 sin (110\pi t)$

$V_{max} = 167 V$

For $V_{max} = 167$,

$sin (110\pi t) = 1$ ...................(1)

That is, $sin\frac{(4k + 1)\pi }{2}$ = 1...............(2)

Comparing equations (1) and (2)

$110\pi t = \frac{(4k+1)\pi }{2}$

$t = \frac{(4k + 1)\pi }{2(110\pi) } \\t = \frac{(4k + 1) }{220 }$

For all positive integer values of k, i.e. k = 0, 1, 2, ........