rectangular coordinates help?

Question

Given the polar coordinates (-sqrt2, 3pi/4) , find the rectangular coordinates of the point.
Can you show work too please? thanks

Answer 1

The polar coordinates are ( length, angle) of a vector. Use sine and cosine to convert to rectangular

x = -sqrt2 sine( 3pi/4)
y = -sqrt2 cosine( 3pi/4)

sine( 3pi/4) = sqrt2
cosine ( 3pi/4) = -sqrt2

so x = -2 and y = 2 or (-2, 2)

Answer 2

Normally r is taken always positive and
-pi<@<=pi for numbers in polar form so
r=-sqrt2 is not usual,but accepting it
x= rcos @ =-sqrt2*(-sqr2)/2 =1
y=r sin @= -sqrt2*(sqrt2)/2=-1
I don´t know how do you mesure angles as normally an angle 3pi/4 belongs to the 2nd quadrant and the point with the usual formules belongs to the fourth
Addendum
looking at the former answer there are afew mistakes
sin and cos are less than 1 and <-1
also the vector formule are
x=rcos @ and y =r sin@