Question

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

Answer 1

`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`

Answer 2

`( 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`