What is the voltage at the 270-degree point of a sine wave with a maximum voltage of 10V?

What is the voltage at the 270-degree point of a sine wave with a maximum voltage of 10V?

• A. -5V
• B. 0V
• C. 10V
• D. -10V

Answer: (D)

The sine wave function can be described mathematically as \( V(t) = V_{max} \times \sin(\theta) \), where \( V_{max} \) is the maximum voltage, and \( \theta \) is the angle in degrees. At 270 degrees, the sine of the angle can be calculated using the sine function. When calculating \( \sin(270^\circ) \), it is important to know the behavior of the sine function at key angles. The sine of 270 degrees corresponds to the value of -1. Since the maximum voltage in this context is given as 10 volts, the calculation follows: \[ V(270^\circ) = 10V \times \sin(270^\circ) = 10V \times (-1) = -10V. \] Therefore, at the 270-degree point of the sine wave, the voltage is -10V. This voltage represents the lowest point on the sine wave, indicating that the waveform has moved below the reference line (0V line) and reached its negative peak, which is consistent with the properties of a sine wave oscillating around zero.

The sine wave function can be described mathematically as ( V(t) = V_{max} \times \sin(\theta) ), where ( V_{max} ) is the maximum voltage, and ( \theta ) is the angle in degrees. At 270 degrees, the sine of the angle can be calculated using the sine function.

When calculating ( \sin(270^\circ) ), it is important to know the behavior of the sine function at key angles. The sine of 270 degrees corresponds to the value of -1. Since the maximum voltage in this context is given as 10 volts, the calculation follows:

[ V(270^\circ) = 10V \times \sin(270^\circ) = 10V \times (-1) = -10V. ]

Therefore, at the 270-degree point of the sine wave, the voltage is -10V. This voltage represents the lowest point on the sine wave, indicating that the waveform has moved below the reference line (0V line) and reached its negative peak, which is consistent with the properties of a sine wave oscillating around zero.