Trigonometria
Seis unidades de trigonometria no triângulo retângulo e no círculo trigonométrico. Você dá nome aos lados de um triângulo retângulo, define seno, cosseno e tangente como razões, aprende os valores exatos de 30°, 45° e 60°, resolve triângulos a partir de um lado e um ângulo, mede alturas que não consegue alcançar, passa para radianos e o círculo trigonométrico e desenha a senoide. O laboratório de trigonometria tem um triângulo retângulo redimensionável, um campo para medir alturas e um círculo trigonométrico ligado ao seu gráfico.
Progresso
- 1Seno, cosseno e tangente
- 2Valores exatos de 30°, 45° e 60°
- 3Resolvendo triângulos retângulos
- 4Medindo alturas com ângulos e sombras
- 5Radianos e o círculo trigonométrico
- 6Gráficos do seno e do cosseno
Fontes deste curso (6)
- OpenStax, Algebra and Trigonometry 2e : 7.2 Right Triangle Trigonometry (sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent, mnemonic SohCahToa; reciprocal functions sec, csc, cot; 3-4-5 example; cos α = 15/17; 30-60-90 sides s, √3s, 2s and 45-45-90 sides s, s, √2s; cofunction identity for complementary angles, cos 34° = sin 56° form; tan 30° = 7/a gives a ≈ 12.1 and c = 7/sin 30° = 14; angle of elevation and depression; tree 30 ft at 57° ≈ 46.2 ft: openstax.org/books/algebra-and-trigonometry-2e/pages/7-2-right-triangle-trigonometry)
- OpenStax Precalculus 2e: 5.1 Angles (one degree is 1/360 of a rotation; one radian intercepts an arc equal to the radius; arc length s = rθ: openstax.org/books/precalculus-2e/pages/5-1-angles)
- 5.2 Unit Circle: Sine and Cosine Functions (cos t = x, sin t = y; Pythagorean Identity cos²t + sin²t = 1: .../pages/5-2-unit-circle-sine-and-cosine-functions)
- 6.1 Graphs of the Sine and Cosine Functions (period 2π; amplitude |A|; period P = 2π/|B| for y = A sin(Bx − C) + D: .../pages/6-1-graphs-of-the-sine-and-cosine-functions)
- MacTutor History of Mathematics, University of St Andrews: "The trigonometric functions" (first known table of chords by Hipparchus about 140 BC, founder of trigonometry; Ptolemy's 360° and Babylonian influence; Aryabhata about 500 used jya for sine; Brahmagupta 628; Abu'l-Wafa 980; jya → jiba → jaib (fold) → Latin sinus; Regiomontanus' De triangulis written about 1464, published 1533; tangent named by Thomas Fincke in 1583; Gunter co-sinus 1620, abbreviation sin 1624; Hérigone first used sin in a book in 1634; Thales used shadows to find the heights of pyramids: mathshistory.st-andrews.ac.uk/HistTopics/Trigonometric_functions/) and "Thales of Miletus" (Hieronymus via Diogenes Laertius: shadows measured when our shadows equal our height; Plutarch's version with a stick at the end of the pyramid's shadow and two triangles in the same ratio: mathshistory.st-andrews.ac.uk/Biographies/Thales/)
- OpenStax Calculus Volume 1, 3.5 Derivatives of Trigonometric Functions (d/dx sin x = cos x with x in radians: openstax.org/books/calculus-volume-1/pages/3-5-derivatives-of-trigonometric-functions)
Data de verificação: 2026-10-17