Question

If sin(x)=1/2, what is cos(x) and tan(x)? explain your steps in complete sentences

Answer 1

sin(x) = 1/2 when x is 30°, 150°, 210°, or 330° (unit circle).

With those angles, the cos(x) is ±√3/2 and the tan(x) is ±√3/3.

Answer 2

`cos(x)=\pm (\sqrt3)/(2)`

`\tan(x)= \pm (1)/(\sqrt3)`

Explanation:

We are given the following information in the question:

`\sin(x) = \displaystyle(1)/(2)`

We use the trigonometry identity:

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

Putting the value, we get,

`\bigg(\displaystyle(1)/(2)\bigg)^2 + \cos^2(x) = 1\\\\\cos^2(x) = (3)/(4)\\\\\cos(x)=\pm (\sqrt3)/(2)`

Formula:

`\tan(x) = \displaystyle(sin(x))/(cox(x))\\\\tan(x) = (\pm (1)/(2))/((\sqrt3)/(2)) = \pm (1)/(\sqrt3)`