# Math Help - Solving Trigonometric Equations

1. ## Solving Trigonometric Equations

Hello again

I just want to know how to solve this trig equation

The instantaneous power in a stove element is given by the equation

Power = V(0)^2/R sin^2 wt
where w = 100pi
V(0) = 340 V
t = time (sec)
R = Resistance (ohms)

a) Find the power for a 48 ohm stove element when t = 0.001 seconds
b) Find the max power
c) Find the time at whcih the max power occurs

2. $P = \frac{V_0^2}{R} \sin^2(\omega t)$

a) $P = \frac{340^2}{48} \sin^2(100\pi \cdot .001) \approx 230 \, \, watts$

b) max power will occur when $\sin(\omega t) = 1$ ...

$P_{max} = \frac{340^2}{48} \cdot 1 \approx 2408 \, \, watts$

c) the initial time that max power occurs will be when $\omega t = \frac{\pi}{2}$

$100\pi t = \frac{\pi}{2}$

solve for t

note that max power will occur periodically when $\omega t$ is equal to odd multiples of $\frac{\pi}{2}$