[tex]\theta=\dfrac{11\pi}6[/tex] behaves the same as [tex]\theta=-\dfrac\pi6[/tex], since [tex]-\dfrac\pi6+2\pi=\dfrac{11\pi}6[/tex]. Recall that [tex]\cos(-x)=\cos x[/tex] and [tex]\sin(-x)=-\sin x[/tex]. Then
[tex]\sin\dfrac{11\pi}6=-\sin\dfrac\pi6=-\dfrac12[/tex]
[tex]\cos\dfrac{11\pi}6=\cos\dfrac\pi6=\dfrac{\sqrt3}2[/tex]
[tex]\tan\dfrac{11\pi}6=\dfrac{\sin\frac{11\pi}6}{\cos\frac{11\pi}6}=-\dfrac1{\sqrt3}[/tex]
[tex]\csc\dfrac{11\pi}6=\dfrac1{\sin\frac{11\pi}6}=-2[/tex]
[tex]\sec\dfrac{11\pi}6=\dfrac1{\cos\frac{11\pi}6}=\dfrac2{\sqrt3}[/tex]
[tex]\cot\dfrac{11\pi}6=\dfrac1{\tan\frac{11\pi}6}=-\sqrt3[/tex]
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[tex]\theta=-\dfrac{7\pi}4[/tex] behaves the sames as [tex]\theta=\dfrac\pi4[/tex], since [tex]\dfrac\pi4-2\pi=-\dfrac{7\pi}4[/tex]. Then
[tex]\sin\left(-\dfrac{7\pi}4}\right)=\sin\dfrac\pi4=\dfrac1{\sqrt2}[/tex]
[tex]\cos\left(-\dfrac{7\pi}4\right)=\cos\dfrac\pi4=\dfrac1{\sqrt2}[/tex]
[tex]\tan\left(-\dfrac{7\pi}4\right)=1[/tex]
[tex]\csc\left(-\dfrac{7\pi}4\right)=\sqrt2[/tex]
[tex]\sec\left(-\dfrac{7\pi}4\right)=\sqrt2[/tex]
[tex]\cot\left(-\dfrac{7\pi}4\right)=1[/tex]
