91Ó°ÊÓ

Find the supplement of each of the following angles. $$ 30^{\circ} $$

For Problems 55 through 68 , find the remaining trigonometric functions of \(\theta\) based on the given information. \(\cot \theta=-\frac{1}{4}\) and \(\sin \theta>0\)

Which answer correctly uses a Pythagorean identity to find \(\sin \theta\) if \(\cos \theta=1 / 4\) and \(\theta\) terminates in QIV? a. \(\sqrt{1+\left(\frac{1}{4}\right)^{2}}\) b. \(\sqrt{1-\left(\frac{1}{4}\right)^{2}}\) c. \(-\sqrt{1+\left(\frac{1}{4}\right)^{2}}\) d. \(-\sqrt{1-\left(\frac{1}{4}\right)^{2}}\)

Show that each of the following statements is an identity by transforming the left side of each one into the right side. $$ \sin \theta \cot \theta=\cos \theta $$

Show that each of the following statements is an identity by transforming the left side of each one into the right side. $$ \sin \theta \sec \theta \cot \theta=1 $$

Find the supplement of each of the following angles. $$ 90^{\circ} $$

For Problems 55 through 68 , find the remaining trigonometric functions of \(\theta\) based on the given information. \(\tan \theta=\frac{a}{b}\) where \(a\) and \(b\) are both positive

Find the supplement of each of the following angles. $$ 135^{\circ} $$

Show that each of the following statements is an identity by transforming the left side of each one into the right side. $$ \cos \theta \csc \theta \tan \theta=1 $$

Find angles \(\theta\) between \(0^{\circ}\) and \(360^{\circ}\) for which the following are true. a. \(\sin \theta=-1\) b. \(\cos \theta=-1\)