What is tanx if 2sinx - 5cosx = 0 ( use right angle triangle ) ?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

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