91Ó°ÊÓ

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \csc (\operatorname{arccsc}(1.0001)) $$

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-\pi \leq x \leq \pi\). $$ \cot (x) \geq-1 $$

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

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

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \csc \left(\operatorname{arccsc}\left(\frac{\pi}{4}\right)\right) $$

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-\pi \leq x \leq \pi\). $$ \cos (x) \geq \sin (x) $$

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

Suppose \(\theta\) is a Quadrant \(\mathrm{I}\) angle with \(\sin (\theta)=x\). Verify the following formulas (a) \(\cos (\theta)=\sqrt{1-x^{2}}\) (b) \(\sin (2 \theta)=2 x \sqrt{1-x^{2}}\) (c) \(\cos (2 \theta)=1-2 x^{2}\)

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-2 \pi \leq x \leq 2 \pi\). $$ \csc (x)>1 $$

In Exercises \(87-106\), find the exact value or state that it is undefined. $$ \arcsin \left(\sin \left(\frac{\pi}{6}\right)\right) $$