Trigonometria

Trigonometria kuvakaappaus  Lataa  Upota
  • Trigonometry
  • Unit circle
  • Sinit

Sisältö

  • Trigonometry
  • Unit circle
  • Sinit
  • Kosinit
  • Tangents

Description

Take a tour of trigonometry using degrees or radians! Look for patterns in the values and on the graph when you change the value of theta. Compare the graphs of sine, cosine, and tangent.

Esimerkkejä oppimistavoitteista

  • Define trig functions for negative angles and angles greater than 90 degrees.
  • Translate between multiple representations of trig functions: as sides of a right triangle inscribed in a unit circle, graph of the function vs. angle, and numerical values of the function.
  • Deduce the sign (+, -, 0) of a trig function for any given angle without a calculator using the unit circle concept.
  • Estimate the value of trig functions for any given angle without a calculator using the unit circle concept.
  • Define exact trig functions for special angles using degrees or radians for angle measures.

Standards Alignment

Common Core - Math

HSF-TF.A.2
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
HSF-TF.A.3
(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number.
HSF-TF.A.4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Version 1.0.22

Teacher Tips

Opettajan opas (pdf) sisältää PhET-tiimin vinkkejä. ( PDF ).

Teacher-Submitted Activities

Trig Tour - Connecting the Unit Circle to the Graph A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Susan Miller L Guided Matematiikka
Trig Tour - Seeing Patterns in a Unit Circle A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Susan Miller L Guided Matematiikka
Trig Tour - Using Reference Angles with a Unit Circle A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Susan Miller L Guided Matematiikka
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López L
YK
Muu Biologia
Fysiikka
Kemia
Matematiikka
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. Diana López L
UG-Intro
Muu Kemia
Matematiikka
Fysiikka
Preguntas de razonamiento para todas las simulaciones HTML5 This contribution was designed by PhET. Diana López K-5
YK
L
UG-Adv
Grad
UG-Intro
Kotiteht
Discuss
Fysiikka
Matematiikka
Kemia
Astronomia
Mapping of PhET and IBDP Physics Jaya Ramchandani L Muu Fysiikka
Figuras y cuerpos geométricos. Andrés Gualberto Palomo Cuevas L Remote
Kotiteht
Matematiikka
Trigonometria: Ciclo e identidades (operações com arcos) Rosalide Carvalho de Sousa e Francisco Régis Vieira Alves L Muu Matematiikka

Kieli Download or Run Tips
Albania All shqip Download Run now Udhëtim trigonometrik
Arabia All العربية Download Run now جولة في حساب المثلثات
Baski All Euskara Download Run now Trig bira
Bosnia All Bosanski Download Run now Trigonometrijske funkcije
Brasilian portugali All português (Brasil) Download Run now Tour Trigonométrico
Englanti All English Download Run now Trig Tour
Espanja All español Download Run now Tour trigonométrico
Espanja (Espanja) All español (España) Download Run now Tour trigonométrico
Espanja (Meksiko) All español (México) Download Run now Tour trigonométrico
Espanja (Peru) All español (Perú) Download Run now Recorrido Trigonométrico
Heprea All עברית Download Run now סיור טריגו
Hindi All हिंदी Download Run now त्रिकोणमिति यात्रा 
Hollanti All Nederlands Download Run now Trigonometrie toer
Irlanti All Gaeilge Download Run now Turas Triantánaithe
Italia All italiano Download Run now Il giro della trigonometria
Japani All 日本語 Download Run now 三角関数
Kannada All Kannada Download Run now ಟ್ರಿಗ್ ಪ್ರವಾಸ
Kazakki All Kazakh Download Run now Тригонометриялық саяхат
Kiina - perinteinen All 中文 (台灣) Download Run now Trig Tour_三角函數之旅
Kiina - yksinkertaistettu All 中文 (中国) Download Run now 三角函数之旅
Kirjanorja All Norsk bokmål Download Run now TrigonometriTur
Korea All 한국어 Download Run now 삼각함수 여행
Kreikka All Ελληνικά Download Run now Περιήγηση στην Τριγωνομετρία
Kroatia All hrvatski Download Run now Trig Tour
Latvia All Latviešu Download Run now Ieskats trigonometrijā
Maori All Maori Download Run now Tawhio Pākoki
Marathi All मराठी Download Run now त्रिकोणमितीची सफ़र
Mongoli All Монгол (Монгол) Download Run now Тригно Аян
Persia All فارسی Download Run now دایره واحد
Puola All polski Download Run now Funkcje trygonometryczne
Ranska All français Download Run now Tour de trigo
Ruotsi All svenska Download Run now Trig Tour
Saksa All Deutsch Download Run now Trigonometrie Tour
Serbia All Српски Download Run now Тригонометријска кружница
Sinhali All Sinhalese Download Run now ත්‍රිකෝණමිතික චාරිකාව (Trig Tour)
Slovakki All Slovenčina Download Run now Trigonometria
Tamili All Tamil Download Run now Trig Tour
Tanska All Dansk Download Run now Enhedscirklen
Telugu All Telugu Download Run now త్రికోణమితి విహార యాత్ర ; అనువాదం: ఉడిత్యాల రమణ
Turkki All Türkçe Download Run now Trigonometri Turu
Ukraina All українська Download Run now Тригонометричний тур
Unkari All magyar Download Run now Szögfüggvények
Valkovenäjä All беларускі Download Run now Трыганаметрычныя функцыі
Venäjä All русский Download Run now Тригонометрические функции (единичная окружность, получение графиков функций)
Vietnam All Tiếng Việt Download Run now Vòng tròn lượng giác

HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iPad:
iOS 12+ Safari
iPad compatible sims

Android:
Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Chromebook:
Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.13+, Safari 13+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

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