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Magazine Problem 163
In Exercises \(155-164\), find the exact value or state that it is undefined. $$ \cos (2 \operatorname{arccot}(-\sqrt{5})) $$
Problem 164
In Exercises \(155-164\), find the exact value or state that it is undefined. $$ \sin \left(\frac{\arctan (2)}{2}\right) $$
Problem 165
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin (\arccos (x)) $$
Problem 166
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \cos (\arctan (x)) $$
Problem 168
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sec (\arctan (x)) $$
Problem 169
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \csc (\arccos (x)) $$
Problem 171
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin (2 \arccos (x)) $$
Problem 172
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \cos (2 \arctan (x)) $$
Problem 173
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin (\arccos (2 x)) $$
Problem 174
In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin \left(\arccos \left(\frac{x}{5}\right)\right) $$
