Question 986424
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If *[tex \Large \sin\phi\ =\ \frac{a}{b}] then *[tex \Large \sin^2\phi\ =\ \frac{a^2}{b^2}], and then by the Pythagorean Identity, *[tex \Large 1\ -\ \cos^2\phi\ =\ \frac{a^2}{b^2}], and then with a little algebra, *[tex \Large \cos^2\phi\ =\ \frac{b^2\ -\ a^2}{b^2}].  Taking the square root: *[tex \Large \cos\phi\ =\ \pm\frac{\sqrt{b^2\ -\ a^2}}{b}].  Adjust the sign based on any given conditions.


Once you know the sine and cosine, the tangent is sine over cosine, cotangent is the reciprocal of tangent, secant is the reciprocal of cosine, and cosecant is the reciprocal of sine.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \