Daily math problems for June 14, 2026 — Trigonometry, Algebra, Quadratic Function

$\bullet$ Use the complementary-angle identity, valid for every $x\in [-1,1]$:

$$\arcsin x+\arccos x=\frac{\pi }{2}$$

$\bullet$ The expression is a constant, so the limit is just that constant:

$$\underset{x\to \sqrt{3}\mathrm{/}2}{\lim }(\arcsin x+\arccos x)=\frac{\pi }{2}$$

Field: commutative ring with unity such that every non-zero element has a multiplicative inverse.

$\mathrm{\Delta }=16-4=12$, $a=-1$, so $f_{\max }=-{\displaystyle \frac{\mathrm{\Delta }}{4a}}=-{\displaystyle \frac{12}{-4}}=3$. The image is $(-\mathrm{\infty },3]$.