Is this right?

Convert the polar coordinate (-14, 5pi/3) to rectangular form.
Does it mean rectangular coordinates and if so can you check my work?

answer:

r=-14
theta=5pi/3

x=-14 cos 5pi/3
x=-14(0.5)
x=-7

y=rsintheta
y=-14 sin 5pi/3
y=-14(-0.866)
y=12.124

(-7,12.124)

I would leave the y value in exact form

y = r sinØ
= -14(√3/2) = -7√3

you also missed the negative sign in your y value

exact point (-7, -7√3)

actually, you are correct, since 5pi/3 is in QIV, so with r = -14, the point is in QII, with y positive.

Yes, you are correct. The rectangular coordinates for the given polar coordinates (-14, 5pi/3) are indeed (-7, 12.124). Well done!

Yes, you are correct. To convert a polar coordinate to rectangular form (rectangular coordinates), you use the following formulas:

x = r * cos(theta)
y = r * sin(theta)

In this case, you are given r = -14 and theta = 5pi/3.

Substituting these values into the formulas, you correctly found:

x = -14 * cos(5pi/3) = -14 * 0.5 = -7

y = -14 * sin(5pi/3) = -14 * (-0.866) = 12.124

Therefore, the rectangular form of the polar coordinate (-14, 5pi/3) is (-7, 12.124). Well done!