Can I use Arduino to alert by sound or LED when it detects a certain voltage
The Arduino boards all have multiple ADC pins (analog inputs).

Assuming that the signal voltage to be measured is guaranteed to not exceed the operating voltage of the Arduino (see note below), you can connect the signal directly to one of the ADC pins. 

Then, in your Arduino sketch, you can poll the ADC in a loop, reading the ADC value on that pin using AnalogRead(), and compare the returned value with the integer value of (V_trigger / V_operating) * 1023. Once this value is returned, your code can invoke the appropriate action, such as lighting up an LED. 

Most Arduino boards do not have on-board sound devices, so for sound, you will need an external speaker, piezo buzzer or similar module. There have been questions on this site and others about output of sound or use of a Piezo buzzer with an Arduino, search and you shall find. 

For the Sine or Cosine values, you would need to calculate those in advance, transform to the AnalogRead() 0-1023 scale using the computation above, and look for a match for the corresponding AnalogRead() value in your code. 

Explanation:

The Arduino AnalogRead() returns values between 0 and 1023, proportional to the voltage at the ADC pin relative to the operating voltage: For a 5 Volt Arduino, 2.5 Volts at the ADC pin returns 511.

Issues:


The ADC value may not be utterly precise due to noise, source voltage impedance, perhaps other factors, hence it might be better to check for a range of values, say 510 to 513 for 2.5 Volts.
If there is any chance that the voltage to be read might exceed the Arduino's operating voltage, the input signal needs to be scaled down using a voltage divider, and / or clamped to 5 Volts using a zener clamp, or a Schottky diode clamp to the 5V / 3.3V pin. Otherwise the Arduino may be toast.
If the voltage source you are reading from has high impedance (multiple kOhms), you will need a voltage follower circuit between this source and the Arduino's ADC pin.




Note: 

Operating voltages for Arduino boards:


5 Volts for most older Arduino board designs including the Uno, Mega, Duemilanove etc
3.3 Volts for the Arduino Due, Fio, some Pro and Pro Mini boards, the LilyPad USB and a few clone boards
2.7 to 5.5 Volts for several Lilypad Arduinos and some other clones.