Question

If tan^-1 4/3 = 0 , find the value of cos theta.

Answer 1

Tan(theta) =4/3 then theta may lie in first quadrant or thrid quadrat.
If theta lies in first quadrant cos(theta) =3/5
If theta lies in thrid quadrant then cos(theta) =-3/5
But tan inverse exists in(-pi/2,pi/2)
Therefore theta lies in first quadrant only.
Hence cos(theta) =3/5

Answer 2

tan ^ -1 4/3 = ¢ , where¢ € ( -π/2 , π/2 )

Therefore,


Tan ¢ = 4/3 .



We know that cos ¢ > 0 when ¢ € ( -π/2 , π/2) .



Therefore,


Cos ¢ = 1/ sec ¢ = 1/ √ 1 + tan²¢ = 1/ √ 1 + 16/9 = 3/5.