Question

give tan 4/5 find the other trigonometric ratio of the angle A

Answer 1

tan = 4/5 =perpendicular /base

so hyp= 4^2 + 5^2 =16 +25 =41 or √41
sin a = p/ hyp =4/√41
cos a = b/h =5/√41
rest u can drive from it

Answer 2

$let \: \tan( \alpha ) = \frac{4}{5} \\ we \: know \: that \: \tan( \alpha ) = \frac{perpendicular}{base} \: \\ say \: perpendicular \: = 4k \\ \: \: \: \: \: \: \: \: base \: =5k \: \\ hypotenuse \: = \sqrt{ ({4k})^{2} + ({5k})^{2} } = \sqrt{41} \times k \\ \\ \sin( \alpha ) = \frac{perpendicular}{hypotenuse} = \frac{4k}{ \sqrt{41}k } = \frac{4}{ \sqrt{41} } \\ \cos( \alpha ) = \frac{base}{hypotenuse} = \frac{5k}{ \sqrt{41}k } = \frac{5}{ \sqrt{41} } \\ \cot( \alpha ) = \frac{1}{ \tan( \alpha ) } = \frac{5}{4} \\ \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } = \frac{ \sqrt{41} }{5} \\ \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } = \frac{ \sqrt{41} }{4}$