Question 1158249
{{{ sin( theta ) = -sqrt(2) / 2 }}}
{{{ sin( theta ) = ( sqrt(2) / sqrt(2) ) * ( -sqrt(2) / 2 ) }}}
{{{ sin( theta ) = -1/sqrt(2) }}}
The sine function is negative in the 3rd and 4th quadrants
{{{ theta = k*( 2pi ) + 4*( pi/4 ) + pi/4 }}}
(1) {{{ theta = k*2pi + 5pi/4 }}}
and
{{{ theta = k*2pi + 8*( pi/4 ) - pi/4 }}}
(2) {{{ theta = k*2pi + 7pi/4 }}}
( 2 solutions )
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In terms of degrees,
(1) {{{ theta = 360k + 225 }}}
(2) {{{ theta = 360k + 315 }}}