tanx = 0.5 find sinx and cosx

We know from the fundamental formula of trigonometry
that:

(sin x)^2 + (cos x)^2 =
1

If we divide by (cos x)^2, both sides, we'll
get:

(sin x/cos x)^2 + 1 = 1/(cos
x)^2

But sin x / cos x = tan
x

(tan x)^2 + 1 = 1/(cos
x)^2

But tan x = 0.5 = 50/100 =
1/2

(1/2)^2 + 1 = 1/(cos
x)^2

5/4 = 1/(cos x)^2

We'll
cross multiply and we'll get:

4 = 5(cos
x)^2

We'll divide by 5:

4/5 =
(cos x)^2

cos x = +/-
2/sqrt5

cos x = +/-
2sqrt5/5

sin x = +/-sqrt(1 -
4/5)

sin x =
+/-sqrt5/5

Conclusion: The
values of sine and cosine have to be both positive, or both negative, in order to obtain
the positive value of tan x = 0.5