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Trigonometric State the three basic trigonometric ratios for the following

Trigonometric State the three basic trigonometric ratios for the following-example-1

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Given


\beta=-(7\pi)/(2)

To find the three basic trigonometric ratios.

Explanation;

It is given that,


\beta=-(7\pi)/(2)

That implies,


\begin{gathered} \sin\beta=sin(-(7\pi)/(2)) \\ =-\sin((7\pi)/(2)) \\ =-sin((6\pi)/(2)+(\pi)/(2)) \\ =-\sin(3\pi+(\pi)/(2)) \\ =-(-sin((\pi)/(2))) \\ =sin(\pi)/(2) \\ =1 \end{gathered}

Also,


\begin{gathered} \cos\beta=cos(-(7\pi)/(2)) \\ =\cos(7\pi)/(2) \\ =-cos(\pi)/(2) \\ =0 \end{gathered}

And,


\begin{gathered} \tan\beta=tan(-(7\pi)/(2)) \\ =-tan((7\pi)/(2)) \\ =-tan((\pi)/(2)) \\ =-\infty \end{gathered}

Hence, the trigonometric ratios are,


sin\beta=1,cos\beta=0,tan\beta=-\infty

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