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I know of two ways to compute the angle between two vectors 1.) cos theta =...

I know of two ways to compute the angle between two vectors

1.) cos theta = (u· v)/(||u||· ||v||)

2.) sin theta = ||u x v||/(||u||· ||v||)

The problem I need help with requires that I show that the two methods produce the same theta value. The vectors I have to work with are u = <-2,2,-2> and v = <4,6,3>. Theoretically, the two theta values should be the same. However, when I did it both ways, the first method produced a theta value of 1.644 radians and the second method produced a value of 1.496 radians. I noticed that these two angles are supplementary. Why did the two methods produce two supplementary angles instead of the same angle? Can you please explain this? Thank you.

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