91Ó°ÊÓ

Simplify each of the following to an expression involving a single trig function with no fractions. \(\frac{1+\cot (t)}{1+\tan (t)}\)

A sector of a circle has a central angle of \(45^{\circ} .\) Find the area of the sector if the radius of the circle is \(6 \mathrm{~cm}\)

A sector of a circle has a central angle of \(30^{\circ} .\) Find the area of the sector if the radius of the circle is \(20 \mathrm{~cm}\)

Simplify each of the following to an expression involving a single trig function with no fractions. \(\frac{1+\sin (t)}{1+\csc (t)}\)

A truck with 32 -in.-diameter wheels is traveling at \(60 \mathrm{mi} / \mathrm{h} .\) Find the angular speed of the wheels in \(\mathrm{rad} / \mathrm{min}\). How many revolutions per minute do the wheels make?

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

Simplify each of the following to an expression involving a single trig function with no fractions. \(\frac{1-\sin ^{2}(t)}{\sin ^{2}(t)}\)

A bicycle with 24 -in.-diameter wheels is traveling at \(15 \mathrm{mi} / \mathrm{h}\). Find the angular speed of the wheels in \(\mathrm{rad} / \mathrm{min}\). How many revolutions per minute do the wheels make?

Prove the identities. $$ \frac{\sin ^{2}(\theta)}{1+\cos (\theta)}=1-\cos (\theta) $$

Prove the identities. $$ \tan ^{2}(t)=\frac{1}{\cos ^{2}(t)}-1 $$