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

5tan(2y+1)=16

2 Answers
Feb 22, 2018

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

Explanation:

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

Feb 22, 2018

y=0.134

Explanation:

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!