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]
