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