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Doubt on inveres trig.

I was doing vector algebra and in a solution to a problem where the angle between the vectors was to be found, i got $$cos \theta$$ = -10 / 102^1/2, so can i write $$theta$$=cos^-1 (10/102^1/2)=cos^-1 ( -10/102^1/2 ). Please explain the former one.

Note by Bhargav Das
4 years, 7 months ago

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Vectors have two components, direction and magnitude (similar to length). When you say $$\cos^{-1} (10/\sqrt{102}$$) you are saying that the $$\cos \theta= \frac{-10}{\sqrt{102}}=\frac{10}{\sqrt{102}}$$. This is obviously incorrect since cosine is the trig function dealing with x values and you have changed the x value from positive to negative.

- 4 years, 7 months ago