Question 123996
Try this:
{{{-5cos(theta) = cos(theta)-3sqrt(3)}}} (I hope I got this right): Subtract {{{cos(theta)}}}from both sides.
{{{-6cos(theta) = -3sqrt(3)}}} Now divide both sides by -6.
{{{cos(theta) = sqrt(3)/2}}}
Now you are looking for the angle theta whose cosine is {{{sqrt(3)/2}}} or:
{{{theta = cos^(-1)(sqrt(3)/2)}}} or
{{{theta = arccos(sqrt(3)/2)}}}
{{{theta = 30}}}degrees.
In radians: {{{theta = (pi)/6}}}Radians.
Check:(Degrees)
{{{-5cos(theta) = cos(theta)-3sqrt(3)}}} Substitute {{{theta = 30}}}
{{{-5cos(30) = cos(30)-3sqrt(3)}}}
{{{-5(0.866) = (0.866)-3(1.732)}}}
{{{-4.33 = -4.33}}}
Check: (Radians)
{{{-5cos(theta) - cos(theta)-3sqrt(3)}}} Substitute{{{theta = (pi)/6}}}
{{{-5cos((pi)/6) = cos((pi)/6)-3sqrt(3)}}}
{{{-5(0.866) = (0.866)-3(1.732)}}}
{{{-4.33 = -4.33}}}