91Ó°ÊÓ

Evaluate the given trigonometric functions directly, without first changing to degree measure. $$\cot (-4.86)$$

Insert the proper sign, \(>\) or \(<\) or \(=,\) between the given expressions. Explain your answers. $$\tan 180^{\circ} \quad \tan 0^{\circ}$$

Solve the given problems. A \(1500-\mathrm{kW}\) wind turbine (windmill) rotates at \(40.0 \mathrm{r} / \mathrm{min} .\) What is the linear velocity of a point on the end of a blade, if the blade is \(35 \mathrm{ft}\) long (from the center of rotation)?

Insert the proper sign, \(>\) or \(<\) or \(=,\) between the given expressions. Explain your answers. $$\sin 270^{\circ} \quad 3 \sin 90^{\circ}$$

Evaluate the given trigonometric functions directly, without first changing to degree measure. $$\csc 6.19$$

Solve the given problems. What is the linear velocity of a point in Charleston, South Carolina, which is at a latitude of \(32^{\circ} 46^{\prime}\) N? The radius of the earth is \(3960 \mathrm{mi}\)

Solve the given problems. Through what total angle does the drive shaft of a car rotate in \(1 \mathrm{s}\) when the tachometer reads \(2400 \mathrm{r} / \mathrm{min} ?\)

Find \(\theta\) to four significant digits for \(0 \leq \theta<2 \pi\). $$\sin \theta=0.3090$$

Solve the given problems. Assume \(\left.0^{\circ}<\theta<90^{\circ} . \text { (Hint: review cofunctions on page } 120 .\right)\) Using the fact that \(\sin 75^{\circ}=0.9659,\) evaluate \(\cos 195^{\circ}\)

Solve the given problems. Assume \(\left.0^{\circ}<\theta<90^{\circ} . \text { (Hint: review cofunctions on page } 120 .\right)\) Using the fact that \(\cot 20^{\circ}=2.747,\) evaluate tan \(290^{\circ}\)