Question

If sin(x) = squareroot 2 over 2 what is cos(x) and tan(x)

Answer 1

Answer:

cos(x) = square root 2 over 2; tan(x) = 1

Step-by-step explanation:

$\frac{\sqrt{2} }{2}$

was, before it was rationalized,

$\frac{1}{\sqrt{2} }$

Therefore,

$sin(x)=\frac{1}{\sqrt{2} }$

The side opposite the reference angle measures 1, the hypotenuse measures square root 2.  That makes the reference angle a 45 degree angle.  From there we can determine that the side adjacent to the reference angle also has a measure of 1.  Therefore,

$cos(x)=\frac{1}{\sqrt{2} }=\frac{\sqrt{2} }{2}$ and

since tangent is side opposite (1) over side adjacent (1),

tan(x) = 1