Question

If tan x = 3/4 and 0◦ ≤ x◦ ≤ 90◦, then cos x =?
Please explain the work behind the solution

Answer 1

Tanx = 3/4 = Y/X = opps/adj

sqrt(3^2+4^2) = 5 = hypotenuse

Cos is adj/hyp

Cosx = 4/5

Answer 2

`tanx=(3)/(4)\\\\tanx=(sinx)/(cosx)\\\\(sinx)/(cosx)=(3)/(4)\to sinx=(3)/(4)cosx\ (*)\\\\\\sin^2x+cos^2x=1\\\\substitute\ (*)\\\\\left((3)/(4)cosx\right)^2+cos^2x=1\\\\(9)/(16)cos^2x+cos^2x=1`


`(15)/(16)cos^2x=1\ /\cdot(16)/(25)\\\\cos^2x=(16)/(25)\\\\cosx=\sqrt(16)/(25)\\\\cosx=(4)/(5)`