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Answer with Explanation: The provided angle theta is:
[tex]\theta=\frac{3}{4}\pi r=135^{\circ}[/tex]According to the unit circle, we have the following:
Therefore the (1) sin(theta) , (2) cos(theta) and (3) tan(theta) are as follows:
(1)
[tex]\begin{gathered} sin(\theta)=\frac{\text{ Opposite}}{\text{ Hypotenuse}} \\ sin(\theta)=\frac{\sqrt{2}}{2}\div1=\frac{\sqrt{2}}{2} \\ sin(\theta)=\frac{\sqrt{2}}{2} \end{gathered}[/tex](2)
[tex]\begin{gathered} cos(\theta)=\frac{\text{ Adjacent}}{\text{ Hypotenuse}}=-\frac{\sqrt{2}}{2}\div1=-\frac{\sqrt{2}}{2} \\ cos(\theta)=-\frac{\sqrt{2}}{2} \end{gathered}[/tex](3)
[tex]\begin{gathered} tan(\theta)=\frac{\text{ Opposite}}{\text{ Adjacent}}=\frac{\sqrt{2}}{2}\div-\frac{\sqrt{2}}{2}=-1 \\ tan(\theta)=-1 \end{gathered}[/tex]The measure of the refrence angle is:
[tex]\theta_r=180^{\circ}-135^{\circ}=45^{\circ}[/tex]In conclusion, therefore the only true statements are as follows:
