Art through the trigonometric and square functions

Arts of trigonometric and square functions 9C Grade Jean Monnet High School Juin 2018 Teacher: Mihaela Gîț

9C Grade

Art of Trigonometric and Square Functions

f(x)=sinx, g(x)=cosx - translated by vector đ??´đ??ľ , A, B ∈ [đ??śđ??ˇ]

f(x)=sinx, g(x)=cosx translated by vector đ??ˇđ??¸ ; the length a of the vector is variable (slider a)

f(x)=sinx, g(x)=cosx - translated by vector đ?‘˘ − rotated with âˆ? ° around his origin

Same conditions. Trace of sinx, cos x

f(x)=sinx, g(x)=cosx - translated by 2 vectors đ?‘Ž and đ?‘¤ − rotated with âˆ? ° around the origin of xOy system.

đ?‘“: −6; 6 → −1; 1 , f(x)=sinx, rotated with âˆ? ° around A(0; 0)

đ?‘“: −1; 6 → −1; 1 , f(x)=sinx, rotated with âˆ? ° around A(0; 0)

đ?‘“, đ?‘”: đ?‘… → −1; 1 , f(x)= sinx, đ?‘” đ?‘Ľ = đ?‘?đ?‘œđ?‘ đ?‘Ľ successive rotations of 45° around A(0; 0)

đ?‘“: đ?‘… → −1; 1 , f(x) = đ?‘?đ?‘œđ?‘ đ?‘Ľ Symmetry and successive rotations of 45° around A(0; 0)

đ?‘“: đ?‘… → −1; 1 , f(x)=sinx, rotated with 45° or 60 ° around A(0; 0)

đ?‘“: đ?‘… → −1; 1 , f(x)=sinx, rotated with 45° around A(0; 0)

đ?‘“: −6; 6 → −1; 1 , f(x)=sinx, rotated with âˆ?= 30đ?‘˜Â° around of the origin of the system xOy

f(x)=sinx, g(x)=tgx - translated by vector đ?‘˘ − rotated with âˆ? ° around his origin Symmetry of sinx to Ox Symmetry of tgx to Oy

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Trigonometric Functions

Art of Square Functions

Rotation around A, with � °

đ?‘“: đ?‘… → đ?‘…, đ?‘“ đ?‘Ľ = đ?‘Ľ 2 − 2đ?‘Ľ +4

Art of Square Functions

Rotation around D, with ∝ ° 𝑓: 𝑅 → 𝑅, 𝑓 𝑥 = 2𝑥 2 𝑔: 𝑅 → 𝑅, 𝑓 𝑥 = 4𝑥 2 ℎ: 𝑅 → 𝑅, 𝑓 𝑥 = 9𝑥 2

Art of Square Functions

Art of Square Functions

𝑓, 𝑔: 𝑅 → 𝑅, f(x)= 𝑥 2 , 𝑔 𝑥 = 𝑥2 − 1 rotations of ∝ ° around A(0; 0) ∝=45° ∝=120° ∝=300° ∝=168°

Rotation around A, with ∝ ° 𝑓: −2; 2 → 𝑅, 𝑓 𝑥 = 𝑥 2 − 1

𝑔: −1; 1 → 𝑅, 𝑓 𝑥 = 𝑥 2 + 4