More Trigonometry

Find sin A if cos A = 0.4

I. Quadrant:

\(\sin{(A)} = + \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = + \sqrt{1-0.4^2}\\ \sin{(A)} = 0.91651513899 \)

IV. Quadrant:

\(\sin{(A)} = - \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = - \sqrt{1-0.4^2}\\ \sin{(A)} = -0.91651513899\)

Find sin A if cos A = 0.4

A = arc cos 0.4

sin A = sin (arc cos 0.4) = 0.9165

A = 0.916515138992

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Hello heureka!

It is "top",
how you represent the trigonometric relationships.
I myself have not considered the arc cos 0.4 is ambiguous,
and your explanation with the unit circle is very obvious.

In my answer is wrong A = 0.916515138992,
correct is sin A = 0.916515138992

Greetings asinus :- )

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Hello asinus!

Thank you very much.