91Ó°ÊÓ

s denotes the length of the arc of a circle of radius \(r\) subtended by the central angle \(\theta .\) Find the missing quantity. Round answers to three decimal places. \(r=2\) inches \(\quad \theta=30^{\circ} \quad s=?\)

A resistor and an inductor connected in a series network impede the flow of an alternating current. This impedance \(Z\) is determined by the reactance \(X\) of the inductor and the resistance \(R\) of the resistor. The three quantities, all measured in ohms, can be represented by the sides of a right triangle as illustrated, so \(Z^{2}=X^{2}+R^{2}\). The angle \(\phi\) is called the phase angle. Suppose a series network has an inductive reactance of \(X=400\) ohms and a resistance of \(R=600\) ohms. (a) Find the impedance \(\underline{Z}\). (b) Find the values of the \(\operatorname{six}\) trigonometric functions of the phase angle \(\phi\).

Is the cotangent function even, odd, or neither? Is its graph symmetric? With respect to what?

The CN Tower The CN Tower, located in Toronto, Canada, is the tallest structure in the Americas. While visiting Toronto, a tourist wondered what the height of the tower above the top of the Sky Pod is. While standing 4000 feet from the tower, she measured the angle to the top of the Sky Pod to be \(20.1^{\circ}\). At this same distance, the angle of elevation to the top of the tower was found to be \(24.4^{\circ}\). Use this information to determine the height of the tower above the Sky Pod.

Finding the Length of a Guy Wire A radio transmission tower is 200 feet high. How long should a guy wire be if it is to be attached to the tower 10 feet from the top and is to make an angle of \(45^{\circ}\) with the ground?

Is the cosecant function even, odd, or neither? Is its graph symmetric? With respect to what?

Washington Monument The angle of elevation of the Sun is \(35.1^{\circ}\) at the instant the shadow cast by the Washington Monument is 789 feet long. Use this information to calculate the height of the monument.

A receiver catches a pass at the 50 -yard line and runs straight towards the end zone. A defender, also standing at the 50 -yard line but 30 yards away from the receiver, decides on an angle of pursuit, \(\theta,\) to tackle the receiver. If \(\cos \theta=0.6,\) where is the defender expecting to tackle the receiver?

A denotes the area of the sector of a circle of radius r formed by the central angle \(\theta .\) Find the missing quantity. Round answers to three decimal places. \(\theta=\frac{1}{4}\) radian, \(A=6\) square centimeters, \(r=?\)

If \(\cos \theta=0.2,\) find the value of $$ \cos \theta+\cos (\theta+2 \pi)+\cos (\theta+4 \pi) $$