Question #8537b

1 Answer
Justin
May 27, 2017

-0.75

Explanation:

By considering the trigonometric identity,

sin^2(x)+cos^2(x)=1sin2(x)+cos2(x)=1
0.6^2+cos^2(x)=10.62+cos2(x)=1
cos(x)=+-0.8cos(x)=±0.8

By considering the CAST rule, because 90< x < 18090<x<180, xx is in quadrant II, therefore cos(x)cos(x) is negative, i.e. cos(x)=-0.8cos(x)=−0.8

By considering the CAST rule, tan(pi-x)=sin(pi-x)/cos(pi-x)=sin(x)/-cos(x)=-tan(x)tan(π−x)=sin(π−x)cos(π−x)=sin(x)−cos(x)=−tan(x)

Therefore tan(pi-x)=sin(x)/-cos(x)=0.6/-0.8=-0.75tan(π−x)=sin(x)−cos(x)=0.6−0.8=−0.75

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