Question 850929
if cos t=0.4, with t in quadrant IV, find tan(t+pi)
cos t=0.4=2/5( In quadrant IV in which cos>0, sin<0, tan<0
{{{sin(t)=-sqrt(1-cos^2(t))=-sqrt(1-4/25)=-sqrt(21/25)=-sqrt(21)/5}}}
tan t=sin/cos={{{-sqrt(21)/2}}}
Identity: {{{tan(t+(pi))=tan((t)+tan(pi))/(1-(tan(t)*tan(pi)))}}}
tan(t+&#960;)=-&#8730;21/2+0/(1-&#8730;21/2*0=-&#8730;21/2
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calculator check:
cos t=0.4
t&#8776;293.58&#730;
t+&#960;&#8776;473.58&#730;
tan(t+&#960;)&#8776;tan(473.58&#730;)&#8776;-2.2910
Exact value=-&#8730;21/2&#8776;-2.2912