Question 1108655
If the terminal side of angle {{{theta}}} , in standard position,
passes through {{{P(x[P],y[P])}}}
{{{tan(theta)}}}{{{"="}}}{{{y[P]/x[P]}}} ; {{{cot(theta)}}}{{{"="}}}{{{x[P]/y[P]}}} ;
{{{sin(theta)}}}{{{"="}}}{{{y[P]/sqrt(x[P]^2+y[P]^2)}}} ; {{{cos(theta)}}}{{{"="}}}{{{x[P]/sqrt(x[P]^2+y[P]^2)}}} ;
{{{sec(theta)}}}{{{"="}}}{{{(cos(theta))^(-1)}}} , and {{{csc(theta)}}}{{{"="}}}{{{(sin(theta))^(-1)}}} .
 
So, in this case,
{{{tan(theta)}}}{{{"="}}}{{{-6/3}}}{{{"="}}}{{{-2}}} ; {{{cot(theta)}}}{{{"="}}}{{{3/(-6)}}}{{{"="}}}{{{-1/2}}} ;
{{{sin(theta)}}}{{{"="}}}{{{(-6)/sqrt(3^2+(-6)^2)}}}{{{"="}}}{{{(-6)/sqrt(9+36) }}}{{{"="}}}{{{(-6)/sqrt(45)}}}{{{"="}}}{{{(-6)/3sqrt(5)}}}{{{"="}}}{{{-2/sqrt(5)}}}{{{"="}}}{{{-2sqrt(5)/5}}} ;
{{{cos(theta)}}}{{{"="}}}{{{3/sqrt(3^2+(-6)^2)}}}{{{"="}}}{{{3/sqrt(9+36) }}}{{{"="}}}{{{3/sqrt(45)}}}{{{"="}}}{{{3/3sqrt(5)}}}{{{"="}}}{{{1/sqrt(5)}}}{{{"="}}}{{{sqrt(5)/5}}} ;
{{{sec(theta)}}}{{{"="}}}{{{(1/sqrt(5))^(-1)}}}{{{"="}}}{{{sqrt(5)}}} , and
{{{csc(theta)}}}{{{"="}}}{{{(-2/sqrt(5))^(-1)}}}{{{"="}}}{{{-sqrt(5)/2}}} .