If cos(t) = − 2/13 and tan(t) > 0, find sin(t) and cos(-t).?

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1 Answer
Jim G.
May 2, 2018

#sint=-sqrt165/13,cos(-t)=-2/13#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)cos(-x)=cosx#

#•color(white)(x)sin^2x+cos^2x=1#

#rArrsinx=+-sqrt(1-cos^2x)#

#"since "cost<0" and "tant>0#

#"this indicates that t is in the third quadrant where"#

#sint<0#

#rArrsint=-sqrt(1-(-2/13)^2)#

#color(white)(rArrsint)=-sqrt(1-(4/169))=-sqrt(165/169)#

#rArrsint=-sqrt165/13#

#cos(-t)=cost=-2/13#

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