# Thread: Showing two equations are identical.

1. ## Showing two equations are identical.

X(t)=1/(√2) (cos(ωt))
Y(t)=cos(ωt+φ)

Demonstrate using trigonometry and algebra that the two equations are identical.

2. Those two equations are not identical. The amplitude of X is 1/(√2), whereas the amplitude of Y is 1. There's no way those two equations are identical. Is this part of a larger problem? If so, please state the original problem, word-for-word.

3. Plot X(t)=1/(√2) (cos(ωt)) and Y(t)=cos(ωt+φ), with ω = 1. Vary φ until you realize what role it plays in the equation.

What role does φ play in the equation? What value of φ makes the two plots identical? Name another value of φ that makes the two plots identical.

Demonstrate using trigonometry and algebra that the two equations are identical.

4. Originally Posted by mandy9008
Plot X(t)=1/(√2) (cos(ωt)) and Y(t)=cos(ωt+φ), with ω = 1. Vary φ until you realize what role it plays in the equation.

What role does φ play in the equation? What value of φ makes the two plots identical? Name another value of φ that makes the two plots identical.

Demonstrate using trigonometry and algebra that the two equations are identical.

As Ackbeet said they cannot be equal as the have different amplitudes!. Here is an animated plot.

In the above plot $\displaystyle \varphi$ goes from $\displaystyle -2\pi < \varphi < 2\pi$