91Ó°ÊÓ

Add or subtract as indicated, then simplify if possible. For part (b), leave your answer in terms of \(\sin \theta\) and/or \(\cos \theta\). a. \(\frac{b}{a}+\frac{1}{b}\) b. \(\frac{\cos \theta}{\sin \theta}+\frac{1}{\cos \theta}\)

Determine whether each statement is true or false. $$ \csc 15^{\circ}<\csc 25^{\circ} $$

Add or subtract as indicated, then simplify if possible. For part (b), leave your answer in terms of \(\sin \theta\) and/or \(\cos \theta\). a. \(\frac{a}{b}-\frac{b}{a}\) b. \(\frac{\sin \theta}{\cos \theta}-\frac{\cos \theta}{\sin \theta}\)

Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38 . Find \(\cos \theta\) if \(\sin \theta=-\frac{1}{4}\) and \(\theta\) terminates in QII.

Add and subtract as indicated. Then simplify your answers if possible. Leave all answers in terms of \(\sin \theta\) and/or \(\cos \theta\). $$ \sin \theta+\frac{1}{\cos \theta} $$

Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38 . If \(\sin \theta=-\frac{4}{5}\) and \(\theta\) terminates in QIII, find \(\cos \theta\).

Add and subtract as indicated. Then simplify your answers if possible. Leave all answers in terms of \(\sin \theta\) and/or \(\cos \theta\). $$ \cos \theta-\frac{1}{\sin \theta} $$

Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38 . If \(\sin \theta=-\frac{5}{13}\) and \(\theta\) terminates in QIV, find \(\cos \theta\)

Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38 . If \(\cos \theta=\frac{\sqrt{3}}{2}\) and \(\theta\) terminates in \(\mathrm{QI}\), find \(\sin \theta\).

Find the distance from the origin out to the point \((3,-4)\).