The cosine of an acute angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.
If cos(x)=1/2, then:
the adjacent side = 1
the hypotenuse = 2
By the Pythagorean theorem:
the opposite side = √(2² - 1²) = √(4-1) = √3
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse, so:
sin(x) = opposite/hypotenuse = √3/2
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side:
tan(x) = opposite/adjacent =√3/1 = √3