Question 1071165
The equation is true if either of these is true:
{{{ 2*cos( theta ) + 1 = 0 }}}
{{{ 2*cos( theta ) = -1 }}}
(1) {{{ cos( theta ) = -1/2 }}}
OR
{{{ tan( theta ) - 1 = 0 }}}
(2) {{{ tan( theta ) = 1 }}}
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(1) {{{ theta = arc cos( -1/2 ) }}}
(1) {{{ theta = 2.0944 }}}
If I divide this by {{{ pi }}} I get {{{ 2/3 }}}, which tells me
(1) {{{ theta  = ( 2*pi )/3 }}}
This is {{{ theta = pi - pi/3 }}}
The cosine is also negative for
{{{ theta = pi + pi/3 }}} which is
{{{ theta = ( 4*pi )/3 }}}
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(2) {{{ theta = arc tan( 1 ) }}}
(2) {{{ theta = .7854 }}}
Dividing by {{{ pi }}}, I get {{{ 1/4 }}}, so
(2) {{{ theta = pi/4 }}}
The tan function is also positive in the 3rd quadrant, so
(2) {{{ theta = pi + pi/4 }}}
(2) {{{ theta = ( 5*pi )/4 }}}
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The solutions are:
{{{ theta }}} = {{{ ( 2*pi )/3 }}}, {{{ (4*pi)/3 }}}, {{{ pi/4 }}}, {{{ (5*pi)/4 }}}
If you can, get another opinion on this also