Question 745763
If tan(theta)= (sqrt5/2), and pi <0<(3pi/2) what are the exact values of cos(theta), sin(theta) and cot(theta) No inverse trig functions.
***
{{{tan(x)=sqrt(5)/2}}} (in quadrant III)
opposite side=-&#8730;5
adjacent side=-2
hypotenuse=&#8730;(2^2+&#8730;5^2)=&#8730;(4+5)=&#8730;9=3
cos(x)=-2/3
sin(x)=-&#8730;5/3
cot(x)=-2/-&#8730;5=(2&#8730;5)/5
..
Check: (with calculator)
tan(x)=&#8730;5/2 (in quadrant III)
x&#8776;228.1897º                    
cos(x)=cos(228.1897º)&#8776;-0.6666..
exact value=-2/3&#8776;-0.6666..
..
sin(x)=sin(228.1897º)&#8776;-0.7454..
exact value=-&#8730;5/3&#8776;-0.7454..
..
cot(x)=cot(228.1897º)&#8776;0.8944..
exact value=5&#8730;5/3&#8776;0.8944..