How do you convert #(2, pi/4)# into rectangular coordinates?

2 Answers
David G.
Jan 18, 2016

#x=2cos(pi/4)=2*0.707=1.414#

#y=2sin(pi/4)=2*0.707=1.414#

Rectangular coordinates are (1.4,1.4)

Explanation:

These coordinates describe a line 2 units long, starting at the origin, #(0,0)#, at an angle of #pi/4# radians anticlockwise (counterclockwise) from the positive axis.

Some find it easier to work in radians, some in degrees. #pi/4# is #45^o#. I'll keep working in radians, since that is how the question is set up.

For rectangular coordinates we need to find the distance of the projection along the x-axis for the first point and along the y-axis for the second.

Draw a diagram. It's crucial.

Now use the definition of trigonometry. The two points are as follows:

#x=2cos(pi/4)=2*0.707=1.414#

#y=2sin(pi/4)=2*0.707=1.414#

Jim G.
Jan 18, 2016

#( sqrt2 , sqrt2 ) #

Explanation:

Using the formulae that links Polar and Cartesian coordinates .

#• x = rcostheta#

#• y = rsintheta #

here r = 2 , #theta = pi/4 #

#rArr x = 2cos(pi/4) = 2 . 1/sqrt2 = 2/sqrt2 xx sqrt2/sqrt2 = sqrt2 #

and y = # 2sin(pi/4) = 2. 1/sqrt2= sqrt2 #

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