X(t)=1/(√2) (cos(ωt))

Y(t)=cos(ωt+φ)

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

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- Feb 7th 2011, 04:22 PMmandy9008Showing 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. - Feb 7th 2011, 04:25 PMAckbeet
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.

- Feb 7th 2011, 04:38 PMmandy9008
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. - Feb 7th 2011, 05:52 PMTheEmptySet
Attachment 20710

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

http://www.mathhelpforum.com/math-he...2&d=1297133353

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