91Ó°ÊÓ

find the exact value or state that it is undefined. $$ \sin \left(\arccos \left(-\frac{1}{2}\right)\right) $$

In Exercises \(129=132\), verify the identity. You may need to consult Sections 2.2 and 6.2 for a review of the properties of absolute value and logarithms before proceeding. $$ -\ln |\sec (\theta)-\tan (\theta)|=\ln |\sec (\theta)+\tan (\theta)| $$

find the exact value or state that it is undefined. $$ \sin \left(\arccos \left(\frac{3}{5}\right)\right) $$

find the exact value or state that it is undefined. $$ \sin (\arctan (-2)) $$

find the exact value or state that it is undefined. $$ \sin (\operatorname{arccot}(\sqrt{5})) $$

As we did in Exercise 74 in Section \(10.2,\) let \(\alpha\) and \(\beta\) be the two acute angles of a right triangle. (Thus \(\alpha\) and \(\beta\) are complementary angles.) Show that \(\sec (\alpha)=\csc (\beta)\) and \(\tan (a)=\cot (\beta)\). The fact that co-fumetions of complementary angles are equal in this case is not an accident. and a more general result will be given in Section 10.4 .

find the exact value or state that it is undefined. \(\sin (\operatorname{arccsc}(-3))\)

Show that \(\cos (\theta)<\frac{\sin (\theta)}{\theta}<1\) also holds for \(-\frac{\pi}{2}<\theta<0\).

find the exact value or state that it is undefined. \(\cos \left(\arcsin \left(-\frac{5}{13}\right)\right)\)

find the exact value or state that it is undefined. \(\cos (\arctan (\sqrt{7}))\)