91Ó°ÊÓ

Use a calculator to find each of the following. Round all answers to four places past the decimal point. $$ \tan 45^{\circ} 19^{\prime} $$

For each expression that follows, replace \(x\) with \(30^{\circ}, y\) with \(45^{\circ}\), and \(z\) with \(60^{\circ}\), and then simplify as much as possible. $$ -2 \sin \left(90^{\circ}-y\right) $$

Use a calculator to find each of the following. Round all answers to four places past the decimal point. $$ \sin 56^{\circ} 40^{\prime} $$

Mark pulls Allison and Mattie in a wagon by exerting a force of 25 pounds on the handle at an angle of \(30^{\circ}\) with the horizontal (Figure 25). How much work is done by Mark in pulling the wagon 350 feet?

For each expression that follows, replace \(x\) with \(30^{\circ}, y\) with \(45^{\circ}\), and \(z\) with \(60^{\circ}\), and then simplify as much as possible. $$ -3 \sin 2 x $$

Expand and simplify: \((\sin \theta-\cos \theta)^{2}\)

Use a calculator to find each of the following. Round all answers to four places past the decimal point. $$ \cos 6^{\circ} 4^{\prime} $$

Subtract: \(\frac{1}{\sin \theta}-\sin \theta\)

For each expression that follows, replace \(x\) with \(30^{\circ}, y\) with \(45^{\circ}\), and \(z\) with \(60^{\circ}\), and then simplify as much as possible. $$ 5 \sin 2 y $$

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