Question

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

Answer 1

`sin(x) =\±(√(2))/(2)`

`tan(x) =\±√(2)`

Explanation:

By definition we know that:

`sin ^ 2 (x) = 1-cos ^ 2 (x)\\\\tan (x) = (sin(x))/(cos (x))`

in this case we know that

`cos(x) =(1)/(2)`

So how:

`sin ^ 2(x) = 1-cos ^ 2(x)`

Substitute the values of cosine in the function

`sin ^ 2 (x) = 1-(1)/(2)`

`sin ^ 2 (x) = (1)/(2)`

`sin(x) =\±\sqrt{(1)/(2)}`

`sin(x) =\±(√(2))/(2)`

Then how:

`tan(x) = (sin(x))/(cos (x))`

Substitute the values of sine and cosine in the function

`tan(x) = \±((√(2))/(2))/((1)/(2))=√(2)`