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!