What are the components of the vector between the origin and the polar coordinate #(1, (11pi)/6)#?

1 Answer
Apr 30, 2016

#((sqrt3/2),(-1/2))#

Explanation:

Convert Polar to Cartesian coordinates using the formulae that link them.

#color(red)(|bar(ul(color(white)(a/a)color(black)( x = rcostheta , y = rsintheta)color(white)(a/a)|)))#

now #(11pi)/6" is an angle in the 4th quadrant "#

where the cos ratio has a positive value and the sin ratio a negative value.

The 'related' acute angle is #(2pi-(11pi)/6)=pi/6#

so #cos((11pi)/6)=cos(pi/6)#
and #sin((11pi)/6)=-sin(pi/6)#

Using the #color(blue)" Exact value triangle for this angle "#
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here r = 1 and #theta=pi/6#

#rArr x=rcostheta=1xxcos(pi/6)=sqrt3/2#

and #y=-rsintheta=1xx-sin(pi/6)=-1/2#