cos(45°)

⚠ Degrees → radians: multiply by $\frac{\pi }{180}$, so the expression becomes $\cos (\frac{45}{180}·\pi )$

Let's calculate: $\cos (\frac{45}{180}\times \pi )$

We divide the numerator and denominator of $\frac{45}{180}$ by the common factor: $45$, which gives the new quotient: $\frac{1}{4}$

$\cos (\frac{1}{4}\times \pi )$

ⓘ The cosine is the x-coordinate (horizontal axis) of the point reached on the unit circle after a rotation of $\frac{1}{4}\times \pi$ radians from the horizontal axis pointing to the right, this is a remarkable value: $\cos (\frac{1}{4}\times \pi )$ = $\frac{\sqrt{2}}{2}$

▶Result:   $\frac{\sqrt{2}}{2}$

The numeric value of: $\frac{\sqrt{2}}{2}$ equals:

$\frac{\approx 1.4142}{2}$

▷ $\approx 0.7071$