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Magazine Problem 82
In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \cos (\theta) \sec (\theta)=1 $$
Problem 82
In Exercises \(81-86\), solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-\pi \leq x \leq \pi\). $$ \sin (x)>\frac{1}{3} $$
Problem 83
In Exercises \(81-86\), solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-\pi \leq x \leq \pi\). $$ \sec (x) \leq 2 $$
Problem 83
Write the given sum as a product. You may need to use an Even/Odd or Cofunction Identity. $$ \sin (9 \theta)-\sin (-\theta) $$
Problem 83
In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \tan (\theta) \cos (\theta)=\sin (\theta) $$
Problem 83
Find the exact value or state that it is undefined. $$ \csc \left(\operatorname{arccsc}\left(-\frac{2 \sqrt{3}}{3}\right)\right) $$
Problem 84
In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \sin (\theta) \csc (\theta)=1 $$
Problem 84
In Exercises \(81-86\), solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-\pi \leq x \leq \pi\). $$ \sin ^{2}(x)<\frac{3}{4} $$
Problem 85
Find the exact value or state that it is undefined. $$ \csc (\operatorname{arccsc}(1.0001)) $$
Problem 85
In Exercises \(81-86\), solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-\pi \leq x \leq \pi\). $$ \cot (x) \geq-1 $$
