How can #(8,-45º)# be converted into rectangular coordinates?

2 Answers
Aug 9, 2017

Answer:

#(4sqrt2, -4sqrt2)#

Explanation:

We're asked to find the rectangular form of a given polar coordinate.

To do this, we use the equations

#ul(x = rcostheta#

#ul(y = rsintheta#

In this case,

  • #r = 8#

  • #theta = -45^"o"#

So we have

#x = 8cos(-45^"o") = ul(4sqrt2#

#y = 8sin(-45^"o") = ul(-4sqrt2#

The coordinate is thus

#color(blue)(ulbar(|stackrel(" ")(" "(4sqrt2, -4sqrt2)" ")|)#

Aug 9, 2017

Answer:

#(4sqrt2,-4sqrt2)#

Explanation:

#"to convert from "color(blue)"polar to rectangular coordinates"#

#"that is "(r,theta)to(x,y)" using"#

#•color(white)(x)x=rcosthetacolor(white)(x);y=rsintheta"#

#"here " r=8" and "theta=-45^@#

#rArrx=8cos(-45)^@=8cos(45)^@=8xx1/sqrt2=4sqrt2#

#y=8sin(-45)^@=-8sin(45)^@=-8xx1/sqrt2=-4sqrt2#

#rArr(8,-45^@)to(4sqrt2,-4sqrt2)#