Given that y<4, find the largest value of y such that #5tan(2y+1)=16#?

Question

#5tan(2y+1)=16#

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Answer 1 · 2018-02-22T14:02:26

#color(blue)(y=(arctan(16/5)-1)/2+pi~~3.27555)#

#5tan(2y+1)=16#

#tan(2y+1)=16/5#

#2y+1=arctan(tan(2y+1))=arctan(16/5)#

#2y+1=arctan(16/5)#

#y=(arctan(16/5)-1)/2~~0.13396color(white)(88)# I Quadrant

#color(blue)(y=(arctan(16/5)-1)/2+pi~~3.27555)color(white)(88)# III Quadrant

Answer 2 · 2018-02-22T14:10:25

#y=0.134#

#5tan(2y+1)=16#

#tan(2y+1)=\frac{16}{5}#

#2y+1=tan^-1(\frac{16}{5})#

#2y+1=1.268#

#2y=0.268#

Simplify:

#y=0.134#

where, #y# represents the angle in radians.

That's it!