At 240 degrees, what is the amplitude of a sine wave with a peak value of 5 volts?

To determine the amplitude of a sine wave at a specific angle, you use the sine function. The formula to calculate the instantaneous value of a sine wave is:

[ V(t) = V_{peak} \times \sin(\theta) ]

where:

• ( V(t) ) is the instantaneous voltage,

• ( V_{peak} ) is the peak value of the sine wave (in this case, 5 volts),

• ( \theta ) is the angle in degrees.

For an angle of 240 degrees, you first convert that angle to radians if necessary for certain calculations or just use its sine value directly. The sine of 240 degrees can be found using the unit circle or a calculator:

[ \sin(240°) = -\frac{\sqrt{3}}{2} \approx -0.866 ]

Now, applying this to the peak voltage:

[ V(240°) = 5 \times \sin(240°) ]

[ V(240°) = 5 \times -0.866 ]

[ V(240°) \approx -4.3 , \text{volts} ]

This indicates that at 240 degrees, the voltage