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Problem 82

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 82

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \csc (\operatorname{arccsc}(\sqrt{2})) $$

Problem 82

In Exercises \(80-85\), write the given sum as a product. You may need to use an Even/Odd or Cofunction Identity. $$ \cos (5 \theta)-\cos (6 \theta) $$

Problem 83

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \csc \left(\operatorname{arccsc}\left(-\frac{2 \sqrt{3}}{3}\right)\right) $$

Problem 83

In Exercises \(80-85\), 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

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

Verify the identity. Assume that all quantities are defined. $$ \tan (\theta) \cos (\theta)=\sin (\theta) $$

Problem 84

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 84

Verify the identity. Assume that all quantities are defined. $$ \sin (\theta) \csc (\theta)=1 $$

Problem 84

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \csc \left(\operatorname{arccsc}\left(\frac{\sqrt{2}}{2}\right)\right) $$

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