Question

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

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

Answer 1

`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

Answer 2

`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!