The value of cos(π)/(4) is:

cos(π)/(4) = sin(π)/(4) = (√(2))/(2).

In ℤ_8, the additive inverse of 3 is:

3 + 5 = 8 ≡ 0 ±od8, so the inverse is 5.

Daily Math Problems — May 12, 2026: Trigonometry, Algebra, Function Analysis

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Problems & worked solutions

RO M1

Problem 1 — The Unit Circle

The value of $\cos \frac{π}{4}$ is:

Show answer & worked solution

A. $\frac{1}{2}$
B. $\frac{\sqrt{2}}{2}$ ✓ correct
C. $\frac{\sqrt{3}}{2}$
D. $1$

$\cos \frac{π}{4} = \sin \frac{π}{4} = \frac{\sqrt{2}}{2}$ .

RO M1

Problem 2 — Modular Arithmetic (ℤₙ)

In $Z_{8}$ , the additive inverse of $\hat{3}$ is:

Show answer & worked solution

A. $\hat{3}$
B. $\hat{0}$
C. $\hat{5}$ ✓ correct
D. $\hat{8}$

$3 + 5 = 8 \equiv 0 (m o d 8)$ , so the inverse is $\hat{5}$ .

RO M1

Problem 3 — Local Extrema

For which value of $a$ does $f (x) = x^{3} - 3 a x + 1$ have a local minimum at $x = 2$ ?

Show answer & worked solution

A. $a = 1$
B. $a = 2$
C. $a = 3$
D. $a = 4$ ✓ correct

$f^{'} (x) = 3 x^{2} - 3 a$ , so $f^{'} (2) = 12 - 3 a = 0 \Rightarrow a = 4$ . Check: $f^{''} (x) = 6 x$ , so $f^{''} (2) = 12 > 0$ , confirming a local minimum.

Problems & worked solutions

RO M1

Problem 1 — The Unit Circle

The value of $\cos \frac{π}{4}$ is:

Show answer & worked solution

A. $\frac{1}{2}$
B. $\frac{\sqrt{2}}{2}$ ✓ correct
C. $\frac{\sqrt{3}}{2}$
D. $1$

$\cos \frac{π}{4} = \sin \frac{π}{4} = \frac{\sqrt{2}}{2}$ .

RO M1

Problem 2 — Modular Arithmetic (ℤₙ)

In $Z_{8}$ , the additive inverse of $\hat{3}$ is:

Show answer & worked solution

A. $\hat{3}$
B. $\hat{0}$
C. $\hat{5}$ ✓ correct
D. $\hat{8}$

$3 + 5 = 8 \equiv 0 (m o d 8)$ , so the inverse is $\hat{5}$ .

RO M1

Problem 3 — Local Extrema

For which value of $a$ does $f (x) = x^{3} - 3 a x + 1$ have a local minimum at $x = 2$ ?

Show answer & worked solution

A. $a = 1$
B. $a = 2$
C. $a = 3$
D. $a = 4$ ✓ correct

$f^{'} (x) = 3 x^{2} - 3 a$ , so $f^{'} (2) = 12 - 3 a = 0 \Rightarrow a = 4$ . Check: $f^{''} (x) = 6 x$ , so $f^{''} (2) = 12 > 0$ , confirming a local minimum.