acos°(sqrt(2)/2)

⚠ The radians are converted into degrees by multiplying them by $\frac{180}{\pi }$ therefore the math expression becomes $\frac{180}{\pi }·\mathrm{acos}\left(\frac{\sqrt{2}}{2}\right)$

Let's evaluate: $\frac{180}{\pi }\times \mathrm{acos}\left(\frac{\sqrt{2}}{2}\right)$

ⓘ acos, asin and atan give the principal angle whose cosine, sine or tangent respectively equals the number, here a remarkable value: $\mathrm{acos}\left(\frac{\sqrt{2}}{2}\right)$ = $\frac{\pi }{4}$

$\frac{180}{\pi }\times \frac{\pi }{4}$

ⓘ The product of fractions is found by multiplying their numerators together and their denominators together: $\frac{180}{\pi }\times \frac{\pi }{4}$ = $\frac{180\pi }{\pi \times 4}$■The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor $\pi$: $\frac{180\pi }{\pi \times 4}$ = $\frac{180}{4}$

$\frac{180}{4}$

ⓘ We simplify the fraction by dividing the numerator and the denominator by $4$, their greatest common divisor: $\frac{180}{4}$ = $45$

▶Result:   $45$