When I use cross products to find an angle of 2 vectors as compared to using dot products, I realised that it's wrong.

Using dot products to find angle

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V = (-3, 1, 0)

W = (1,2,0)

Formula: cosΘ = V dot W /( |V||W| )

=> cosΘ = -1 / √50

=> cosΘ = -0.141421

Inverse of cos gives 98.13° which is the correct angle.

Using cross products to find angle

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V = (-3, 1, 0)

W = (1,2,0)

Formula: |VxW| = |V||W|sinΘ

=> sinΘ = |VxW| / |V||W|

=> sinΘ = 7 / √50

=> sinΘ = 0.989949

Inverse of sin gives 81.869898° which is a wrong angle.

But if 180°-81.869898° gives the right answer.

Why is that so? Is it something wrong with the formula?

Please advice, thank you so much for your time.