The voltage of the electric supply at our homes varies with time as which of the following trigonometric functions?
1. Tangent
2. Sine
3. Cosine
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both 2 and 3
The mains supply is an alternating voltage. It rises to a peak \( v_m \), falls through zero to \( -v_m \) and repeats smoothly. So it varies sinusoidally with time, \( v=v_m\sin\omega t \).
1. Tangent — False. \( \tan\omega t \) has no largest value. It becomes infinite at \( \omega t=\pi/2 \) and jumps from \( +\infty \) to \( -\infty \). But the supply voltage always stays between \( +v_m \) and \( -v_m \).
2. Sine — True. Taking \( t=0 \) at an instant when the voltage is zero and rising, the supply voltage is \( v=v_m\sin\omega t \).
3. Cosine — True. \( \cos\omega t=\sin(\omega t+\pi/2) \) is the same sinusoidal curve shifted in time. Taking \( t=0 \) at a peak of the voltage gives \( v=v_m\cos\omega t \).
NCERT (2026-27):
Introduction – “… The electric mains supply in our homes and offices is a voltage that varies like a sine function with time.”