Find the value of Tan 19π/4?

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Answer 1 · 2018-04-25T07:06:49

#tan((19pi)/4)=-1#

We note that,

#color(blue)(pi-theta,3pi-theta,5pi-theta,...,(2k+1)pi-theta,toII^(nd) Quadrant#

#color(blue)(So, tantheta < 0#

#color(blue)(=>tan(pi-theta)=tan(3pi-theta)=tan(5pi-theta)=...=- tantheta#

We have,

#tan((19pi)/4)=tan((20pi-pi)/4)=tan((20pi)/4-pi/4)#

#:.tan((19pi)/4)=color(blue)(tan(5pi-pi/4)#

#:.tan((19pi)/4)=color(blue)(-tan(pi/4))=-1#