6.1 Polar coordinates

(Calculator) Rewrite the following coordinates as polar coordinates. Express all angles in radians.

(a) [math](-3,5)[/math]

(b) [math](6,1)[/math]

(c) [math](-1,-3)[/math]

(d) [math](4,-2)[/math]

(Calculator) Rewrite the following polar coordinates as rectangular coordinates:

(a) [math][2,-38^\circ][/math]

(b) [math][5,123^\circ][/math]

(c) [math][7,0][/math]

(d) [math][9,2][/math]

Lindsey was standing under a bus stop. To kill time, she walked 3 meters with a direction of [math]40^\circ[/math], and then jumped 10 times. Next, she walked 8 meters with a direction of [math]160^\circ[/math] and then sang a song. Given that the bus stop is the origin, find Lindsey’s location. If [math][r,\theta][/math] represents Lindsey’s location, what are [math]r[/math] and [math]\theta[/math]?

(Calculator) Find the area of triangle [math]ABC[/math] where [math]A\left[3,\dfrac{\pi}{6}\right], B\left[4,\dfrac{7\pi}{4}\right][/math] and [math]C[5,\pi][/math].
Hint: Plot [math]A, B[/math], and [math]C[/math] on the polar coordinate plane.