Simplify \( \frac{\cos ^{2}(t)}{\sin ^{2}(t)+\cos ^{2}(t)} \) to an expression involving a single trig function with no fractions.

If \( \sin (\theta)=-\frac{2}{3} \), and \( \theta \) is in quadrant IV, then find (a) \( \cos (\theta)=\square \) (b) \( \tan (\theta)=\square \) (c) \( \sec (\theta)=\square \) (d) \( \csc (\theta)=\square \) (e) \( \cot (\theta)=\square \)

If \( \theta=-\frac{2 \pi}{3} \), then find exact values for the following: \( \sin (\theta)=\square \) \( \cos (\theta)=\square \) \( \tan (\theta)=\square \) \( \csc (\theta)=\square \) \( \sec (\theta)=\square \) \( \cot (\theta)=\square \)

Without using a calculator, compute the sine and cosine of \( 120^{\circ} \) by using the reference angle. What is the reference angle? In what quadrant is this angle? \( \sin \left(120^{\circ}\right)=\square \) degrees. \( \cos \left(120^{\circ}\right)=\square \) (Type sqrt(2) for \( \sqrt{2} \) and sqrt(3) for \( \sqrt{3} \).)

\( \frac { \sin A } { 1 + \cos A } + \frac { 1 - \operatorname { cosec } A } { \sin A } = 2 \operatorname { cosec } A \)

Find the exact values of the six trig functions. Give an exact answer. No decimals!!! \( \sin \left(300^{\circ}\right)=\square \) \( \cos \left(300^{\circ}\right)=\square \) \( \tan \left(300^{\circ}\right)=\square \) \( \csc \left(300^{\circ}\right)=\square \) \( \sec \left(300^{\circ}\right)=\square \) \( \cot \left(300^{\circ}\right)=\square \)