Question 1137903

note:
Quadrant 1: All are positive
Quadrant 2: Sine is positive
Quadrant 3: Tangent is positive
Quadrant 4: Cosine is positive

given:

{{{sin (theta)=sqrt(2/3) >0}}} ,theta must lie in the {{{1st}}} or {{{2nd}}} quadrant

{{{cos(theta) > 0}}}.....which it is, theta must lie in the {{{1st}}} or{{{ 4th}}} quadrant

 

common for both {{{sin (theta) >0}}} and {{{cos(theta) >0}}} is {{{1st}}} quadrant

{{{sin (theta)=sqrt(2/3) =0.816496580927726}}}

{{{theta=sin^-1 (0.816496580927726)}}}

{{{theta=54.7356103172453}}}°

{{{cos(theta) =cos(54.7356103172453)=0.577350269189626}}}=>{{{cos(theta)>0}}}