Question 979965
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin(a)\ =\ \frac{3}{5}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(a)\ =\ \frac{9}{25}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ \sin^2(a)\ =\ 1\ -\ \frac{9}{25}\ =\ \frac{16}{25}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos^2(a)\ =\ \frac{16}{25}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(a)\ =\ \pm\sqrt{\frac{16}{25}}]


But it is given that *[tex \Large \cos(a)\ <\ 0], so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(a)\ =\ -\frac{4}{5}]


From here, you can find the value of any of the other four functions by use of the following identities:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan\varphi\ =\ \frac{\sin\varphi}{\cos\varphi}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cot\varphi\ =\ \frac{1}{\tan\varphi}\ =\ \frac{\cos\varphi}{\sin\varphi}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sec\varphi\ =\ \frac{1}{\cos\varphi}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \csc\varphi\ =\ \frac{1}{\sin\varphi}]


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

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