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Magazine Problem 90
Use fundamental identities to find the values of the trigonometric functions for the given conditions. $$\csc \theta=5 \text { and } \cot \theta<0$$
Problem 91
Use fundamental identities to find the values of the trigonometric functions for the given conditions. $$\sec \theta=-4 \text { and } \csc \theta>0$$
Problem 92
Use fundamental identities to find the values of the trigonometric functions for the given conditions. $$\sin \theta=\frac{2}{5} \text { and } \cos \theta<0$$
Problem 93
Rewrite the expression in nonradical form without using absolute values for the indicated values of \(\theta .\) $$\sqrt{\sec ^{2} \theta-1} ; \quad \pi / 2<\theta<\pi$$
Problem 94
Rewrite the expression in nonradical form without using absolute values for the indicated values of \(\theta .\) $$\sqrt{1+\cot ^{2} \theta}, \quad 0<\theta<\pi$$
Problem 95
Rewrite the expression in nonradical form without using absolute values for the indicated values of \(\theta .\) $$\sqrt{1+\tan ^{2} \theta} ; \quad 3 \pi / 2<\theta<2 \pi$$
Problem 96
Rewrite the expression in nonradical form without using absolute values for the indicated values of \(\theta .\) $$\sqrt{\csc ^{2} \theta-1} ; \quad 3 \pi / 2<\theta<2 \pi$$
Problem 97
Rewrite the expression in nonradical form without using absolute values for the indicated values of \(\theta .\) $$\sqrt{\sin ^{2}(\theta / 2)} ; \quad 2 \pi<\theta<4 \pi$$
Problem 98
Rewrite the expression in nonradical form without using absolute values for the indicated values of \(\theta .\) $$\sqrt{\cos ^{2}(\theta / 2)} ; \quad 0<\theta<\pi$$
