If cosine of x equals 1 over 2, what is sin(x) and tan(x)? Explain your steps in simple complete sentences

Answer:[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex][tex]tan(x) =\±\sqrt{2}[/tex]Step-by-step explanation:By definition we know that:[tex]sin ^ 2 (x) = 1-cos ^ 2 (x)\\\\tan (x) = \frac{sin(x)}{cos (x)}[/tex]in this case we know that[tex]cos(x) =\frac{1}{2}[/tex]So how:[tex]sin ^ 2(x) = 1-cos ^ 2(x)[/tex]Substitute the values of cosine in the function[tex]sin ^ 2 (x) = 1-\frac{1}{2}[/tex][tex]sin ^ 2 (x) = \frac{1}{2}[/tex][tex]sin(x) =\±\sqrt{\frac{1}{2}}[/tex][tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]Then how:[tex]tan(x) = \frac{sin(x)}{cos (x)}[/tex]Substitute the values of sine and cosine in the function[tex]tan(x) = \±\frac{\frac{\sqrt{2}}{2}}{\frac{1}{2}}=\sqrt{2}[/tex]