What are the components of the vector between the origin and the polar coordinate #(1, (5pi)/4)#?

1 Answer
Jan 15, 2016

Answer:

The #x# component is: #cos((5pi)/4)#
The #y# component is: #sin((5pi)/4)#

Explanation:

Remembering our trigonometry, the vertical component of a vector is given by
#r*sin(theta)# where #r# is the length of the line,
and the horizontal component by
#r*cos(theta)#

https://en.wikipedia.org/wiki/Trigonometry

in the polar coordinate #(1,(5pi)/4)#, #r# is 1, and the angle #theta = (5pi)/4#.

Hence:
The #x# component is: #cos((5pi)/4)#
The #y# component is: #sin((5pi)/4)#

In this case, #(5pi)/4# is midway in the lower left quadrant, or #135^@#, so both are equal to #-1/sqrt2#