How do you determine the exact coordinates of a point on the terminal arm of the angle in standard position given 45 degrees?

1 Answer
Somebody N.
Feb 26, 2018

See below.

Explanation:

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By looking at the diagram we can find a relationship between the Cartesian coordinates and the angular measurement.

Point #bbP# has Carteaian coordinates #(x,y)#, and polar coordinates #(r,theta)#, we are only concerned with Cartesian for this. We can see that these correspond to the sine and cosine functions in the following way.

#x=rcos(theta)#

#y=rsin(theta)#

Where #bbr# is the radius, for a unit circle this will be #bb1#. The cordinates of #bbP# are now:

#(rcos(theta),rsin(theta))#

So using this idea:

For:

radius #bb1# and #theta=45^@#, we have:

#x=cos(45^@)=sqrt(2)/2#

#y= sin(45^@)=sqrt(2)/2#

So coordinates are:

#(sqrt(2)/2,sqrt(2)/2)#

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