What is tanx if 2sinx - 5cosx = 0 ( use right angle triangle ) ?
According to the Pythagorean theorem in a right angle triangle:
(sin x)^2 + (cos x)^2 = 1
If we'll divide the expression by (cos x)^2, we'll get:
(sin x)^2/(cos x)^2 + 1 = 1/(cos x)^2
(tan x)^2 = 1/(cos x)^2 - 1
By definition, the trigonometric function tangent is a ratio between the opposite cathetus and the adjacent cathetus.
2sinx - 5cosx = 0
2sin x = 5cos x
If we divide the entire expression by 5 cos x, we'll get:
(2/5) (sin x/cos x) = 1
We'll substitute the ratio sin x/cos x = tan x
(2/5)* tan x = 1
tan x = 5/2