Question 1092900
Note that {{{ x }}} is in the 3rd quadrant, so actually
{{{ tan(x) = (-20)/(-21) }}}
{{{ (-20)/(-21) = 20/21 }}}
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The length of the rotating vector is:
{{{ c = sqrt( 20^2 + 21^2 ) }}}
{{{ c = sqrt( 400 + 441 ) }}}
{{{ c = sqrt( 841 ) }}}
{{{ c = 29 }}}
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Since a general rule is: {{{ sin( x + pi/2 ) = cos( x ) }}}
{{{ cos( x ) = -21/29 }}}
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Note that if {{{ pi < x < 3pi/2 }}}, then
{{{ x + pi/2 }}} is an angle in the 4th quadrant
where the sin function is negative