A coil of wire rotating in a magnetic field induces a voltage given by e = 20 sin(piT/4 - pi/2) where t is time in seconds.?

I'm going to express in degrees:

10*√2 = 20*sin(45t - 90)

10*√2/20 = ½*√2 = sin(45t - 90)

arcsin(0.7071) = 45° = 45t - 90°

135° = 45t so t = 3 is the answer choice C.

OR using radians

arcsin ½*√2 = π/4 = π*t/4 - π/2

π/4+π/2 = π*t/4

4*π/4+4*π/2 = π*t

π+2*π = π*t = 3*π or t = 3 same answer.

10√2 = 20*(√2)/2 = 20*sin 45°

in other words :

(180°*t-360°)/4 = 45°

180°*t = 360°+180°

t = 3 sec

e = 10*sqrt(2) = 20sin(pi*t/4 - pi/2) -->> sin(pi*t/4 - pi/2) = sqrt(2)/2

Sin(x) = sqrt(2)/2 when x = +/- pi/4 radians (+/- 45 degrees) so

pi/4 = pi*t/4 - pi/2 --> 1/4 = t/4 - 1/2 --> t = 3/4

-pi/4 = pi*t/4 -pi/2 ---> -1/4 = t/4 - 1/2 ----> t = 1/4 --> this is the answer