I'm reading on a distance, and this is the first time I just got totally stuck. I need help really fast!

It's probably really easy.

I understand that sin^2v + cos^2v = 1

Now for an example:

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What is Sin(v) if cos(v) = -(24/25)?

I'm doing sin^2(v) = 1-(-(24/25)^2) = 1.9216 which ofcourse is wrong (answer is -(7/25)).

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Example 2:

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1/cos^2(v) = 1 + tan^2(v)

This is how the solution is written in the book:

1+tan^2(v) = 1 + (sin^2(v)/cos^2(v)) = (cos^2(v) + sin^2(v))/cos^2(v)

For some reason I don't get how 1 becomes cos^2(v).

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What am I doing wrong? Appreciate help!!