Question 880169
given that cot(theta)=&#8730;3 and cos( theta) < 0 . without finding the angle (theta ). find all other trigonometric ratios for theta.
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You are working with a reference right triangle in quadrant III in which cos<0, cot >0, sin<0, tan>0
hypotenuse of reference right triangle in quadrant III=&#8730;(&#8730;3)^2+1^2)=&#8730;(3+1)=&#8730;4=2
cot(theta)=&#8730;3
tan(theta)=1/&#8730;3=&#8730;3/3
sin(theta)=-1/2
csc(theta)=-2
cos(theta)=-&#8730;3/2
sec(theta)=-2/&#8730;3=-2&#8730;3/3