Respuesta :

Given: The trigonometry shown in the image

To Determine: The exact values of the six trogonometric functions of each angle shown

Solution

It can be observed that

Therefore

[tex]\begin{gathered} sin\theta=-1 \\ cos\theta=-\sqrt{2} \end{gathered}[/tex][tex]tan\theta=\frac{sin\theta}{cos\theta}=\frac{-1}{-\sqrt{2}}=\frac{1}{\sqrt{2}}[/tex][tex]\begin{gathered} csc\theta=\frac{1}{sin\theta}=\frac{1}{-1}=-1 \\ sec\theta=\frac{1}{cos\theta}=\frac{1}{-\sqrt{2}}=-\frac{1}{\sqrt{2}} \\ cot\theta=\frac{1}{tan\theta}=\frac{1}{\frac{1}{\sqrt{2}}}=1\times\sqrt{2}=\sqrt{2} \end{gathered}[/tex]

Ver imagen RonneyS642504

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