Chapter 9: Polar Coordinates, Vectors

The letters r and $\theta$represent polar coordinates. Write each equation using rectangular coordinates $\left(x,y\right)$.

$r=\sin \theta +1$

In Problems 71–80, graph each polar equation. Verify your graph using a graphing utility.

$r=\frac{3}{\theta }$

Work

Find the work done by a force of $3$newtons acting in the direction $2i+j+2k$in moving an object 2 meters fromrole="math" localid="1646804269936" $(0,0,0)$ to$(0,2,0)$.

Finding the Actual Speed and Direction of an Aircraft A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles per hour (mi/hr) headed due north. The jet stream is 100 mi/hr in the northeasterly direction.

(a) Express the velocity $v_a$of the 747 relative to the air and the velocity $v_w$of the jet stream in terms of i and j.

(b) Find the velocity of the 747 relative to the ground.

(c) Find the actual speed and direction of the 747 relative to the ground.

The letters r and $\theta$represent polar coordinates. Write each equation using rectangular coordinates $\left(x,y\right)$.

$r^2=\cos \theta$

In Problems 71–80, graph each polar equation. Verify your graph using a graphing utility.

$r=csc\theta -2$

Finding the Actual Speed and Direction of an Aircraft An Airbus A320 jet maintains a constant airspeed of 500 mi/hr headed due west. The jet stream is 100 mi/hr in the southeasterly direction.

(a) Express the velocity $v_a$of the A320 relative to the air and the velocity $v_w$of the jet stream in terms of i and j.

(b) Find the velocity of the A320 relative to the ground.

(c) Find the actual speed and direction of the A320 relative to the ground.

The letters r and $\theta$represent polar coordinates. Write each equation using rectangular coordinates $(x,y)$.

$r=\sin \theta -\cos \theta$

Work

Find the work done by a force of $1$newton acting in the direction $2i+2j+k$in moving an object 3 meters from $(0,0,0)$to$(1,2,2)$.

In Problems 71–80, graph each polar equation. Verify your graph using a graphing utility.

$r=\sin \theta .\tan \theta$