# If sin X = 4/5, what is tan X?

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It is given that `sin X = 4/5` .

Use the identity `sin^2X + cos^2X = 1`

=> `(4/5)^2 + cos^2 X = 1`

=> `cos^2 X = 1 - 16/25`

=> `cos^2 X = 9/25`

=> `cos X = 3/5 or cos X = -3/5`

This can give two values of tan X, `(sin X)/(cos X)` can be `(4/5)/(3/5) = 4/3`

tan X could be `(4/5)/(-3/5) = -4/3` but it is seen that `sin(tan^-1(-4/3)) = -4/5`

**The value of **`tan X = 4/3`

If sin X = 4/5, what is tan X?

sin of an angle is Perpendicual divided by Hypotenuse for the angle of a right-angled triangle at base.

Let "k" be multiplier so that

In this case, the Perpendicular = 4k and Hypotenuse = 5k

Fo above,

The base of triangle = sqrt((Hypotenuse)^2-(Perpedicular)^2)

The base of triangle = sqrt((5k)^2-(4k)^2) = sqrt(25-16)*k = 3k

tanX = perpendicular/base = 4/3

**The value of tan X = 4/3**** **when sin X = 4/5