What is cos x if tan x=6/11?Solve using right triangle

We'll write the fundamental formula in
trigonometry:

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

If you divide the above formula with (cos
x)^2

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

But the tangent function is the ratio between sin
x/cos x, so (sin x)^2/(cos x)^2 = (tan x)^2

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

(cos x)^2[(tan x)^2+ 1] =
1

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

cos x = sqrt1/[(tan x)^2+
1]

cos x = sqrt[1/[(6/11)^2 +
1]

cos x = sqrt[1/[(36/121) +
1]

cos x =
sqrt[1/(36+121)/121]

cos x = sqrt
(121/157)

cos x = 11/sqrt
157