--- title: Trigonometric Functions - Example of Finding Angles description: "A trigonometric functions example: sine, cosine, and tangent of a given angle in a right triangle." url: https://astra-ai.co/videos/trigonometry/trigonometric-functions/trigonometric-functions-example/ locale: en type: video-lesson keywords: - trigonometric functions - sine cosine tangent - worked example - right triangle published: 2026-10-01T10:00:13.701Z updated: 2026-10-04T22:03:10.177Z alternates: bg: https://astra-ai.co/bg/videos/trigonometriya/trigonometrichni-funktsii/trigonometrichni-funktsii-primer/ br: https://astra-ai.co/br/videos/trigonometria/capitulo-matematica-046/video-matematica-101/ cs: https://astra-ai.co/cs/videos/trigonometrie/goniometricke-funkce/trigonometricke-funkce-priklad/ da: https://astra-ai.co/da/videos/trigonometri/trigonometriske-funktioner/trigonometriske-funktioner-eksempel/ de: https://astra-ai.co/de/videos/trigonometrie/winkelfunktionen/winkelfunktionen-ein-beispiel/ el: https://astra-ai.co/el/videos/trigonometria/trigonometrikes-synartiseis/trigonometric-functions-example/ en: https://astra-ai.co/videos/trigonometry/trigonometric-functions/trigonometric-functions-example/ en-IN: https://astra-ai.co/en-IN/videos/trigonometry/chapter-b232e89b/trigonometric-functions-example/ en-PH: https://astra-ai.co/en-PH/videos/trigonometry/chapter-b232e89b/lesson-98e9bec7/ es: https://astra-ai.co/es/videos/trigonometria/funciones-trigonometricas/calcular-angulos-con-trigonometria/ es-AR: https://astra-ai.co/es-AR/videos/trigonometria/capitulo-40/leccion-de-matematicas-101/ es-CL: https://astra-ai.co/es-CL/videos/trigonometria/capitulo-40/leccion-de-matematicas-101/ es-PE: https://astra-ai.co/es-PE/videos/trigonometria/capitulo-video-b232e89b/leccion-de-video-98e9bec7/ et: https://astra-ai.co/et/videos/trigonomeetria/trigonomeetrilised-funktsioonid/trigonomeetrilised-funktsioonid-naide/ fi: https://astra-ai.co/fi/videos/trigonometria/trigonometriset-funktiot/trigonometriset-funktiot-esimerkki/ fr: https://astra-ai.co/fr/videos/trigonometrie/fonctions-trigonometriques/exemple-de-calcul-avec-les-fonctions-trigonometriques/ hr: https://astra-ai.co/hr/videos/trigonometrija/trigonometrijske-funkcije/trigonometrijske-funkcije-primjer/ hu: https://astra-ai.co/hu/videos/trigonometria/trigonometriai-fuggvenyek/trigonometriai-fuggvenyek-pelda/ id: https://astra-ai.co/id/videos/trigonometri/fungsi-trigonometri/fungsi-trigonometri-contoh/ it: https://astra-ai.co/it/videos/trigonometria/funzioni-trigonometriche/funzioni-trigonometriche-esempio/ ja: https://astra-ai.co/ja/videos/trigonometry-ja/40/101/ km: https://astra-ai.co/km/videos/trigonometry/chapter-b232e89b/lesson-98e9bec7/ ko: https://astra-ai.co/ko/videos/trigonometry-ko/40/101/ lo: https://astra-ai.co/lo/videos/lo-b77f8f5c/lo-b232e89b/lesson-98e9bec7/ lt: https://astra-ai.co/lt/videos/trigonometrija/trigonometrines-funkcijos/pamoka-98e9bec7/ lv: https://astra-ai.co/lv/videos/trigonometrija/trigonometriskas-funkcijas/stunda-98e9bec7/ ms: https://astra-ai.co/ms/videos/trigonometry/bab-46-matematik-asas/pelajaran-101/ ms-BN: https://astra-ai.co/ms-BN/videos/trigonometri/bab-b232e89b/pelajaran-98e9bec7/ mx: https://astra-ai.co/mx/videos/trigonometria/capitulo-40/leccion-101/ my: https://astra-ai.co/my/videos/my-b77f8f5c/my-b232e89b/lesson-98e9bec7/ nl: https://astra-ai.co/nl/videos/trigonometrie/trigonometrische-functies/goniometrische-functies-voorbeeld/ no: https://astra-ai.co/no/videos/trigonometri/trigonometriske-funksjoner/trigonometriske-funksjoner-eksempel/ pl: https://astra-ai.co/pl/videos/trygonometria/funkcje-trygonometryczne/funkcje-trygonometryczne-przyklad/ pt: https://astra-ai.co/pt/videos/trigonometria/funcoes-trigonometricas/funcoes-trigonometricas-exemplo/ pt-TL: https://astra-ai.co/pt-TL/videos/trigonometria/capitulo-de-video-040/licao-de-video-101/ ro: https://astra-ai.co/ro/videos/trigonometrie/functii-trigonometrice/functii-trigonometrice-exemplu/ sk: https://astra-ai.co/sk/videos/trigonometria/kapitola-040/lekcia-101/ sl: https://astra-ai.co/sl/videos/trigonometrija/trigonometricne-funkcije/trigonometricne-funkcije-primer/ sr: https://astra-ai.co/sr/videos/trigonometrija/poglavlje-040/lekcija-101/ sv: https://astra-ai.co/sv/videos/trigonometri/trigonometriska-funktioner/trigonometriska-funktioner-exempel/ th: https://astra-ai.co/th/videos/trigonometry/bot-46-fangchan-trikon/botrian-101/ tr: https://astra-ai.co/tr/videos/trigonometri/bolum-040/ders-101/ uk: https://astra-ai.co/uk/videos/uk-topic-09/uk-chapter-46/uk-lesson-98e9bec7/ vi: https://astra-ai.co/vi/videos/vi-topic-09/vi-chapter-46/ham-luong-giac-vi-du/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-009/shuxue-zhang-046/shuxue-kecheng-101/ zh-TW: https://astra-ai.co/zh-TW/videos/trigonometry/chapter-b232e89b/lesson-98e9bec7/ --- # Trigonometric Functions – Example > This trigonometric functions example finds sine, cosine, and tangent for an angle in a right triangle. ## BASICS OF TRIGONOMETRIC FUNCTIONS Trigonometric functions in a right-angled triangle are defined for acute angles (less than 90°) and are based on the ratios between the lengths of the sides: - **SINE (sin)** is the ratio of the length of the side opposite the angle to the length of the hypotenuse. - **COSINE (cos)** is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. - **TANGENT (tan)** is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. ## CALCULATING ANGLES: If we know the lengths of two sides of a right-angled triangle, we can use one of these functions to calculate an unknown angle. The procedure is as follows: - **CHOOSE THE CORRECT TRIGONOMETRIC FUNCTION:** First, determine which trigonometric function is appropriate based on the known sides. For example, if we know the length of the hypotenuse and the side opposite the angle, we use sine. - **USE THE INVERSE FUNCTION:** To calculate the angle from the ratio, use the inverse trigonometric function (e.g., arcsin, arccos, arctan, also denoted as sin⁻¹, cos⁻¹, tan⁻¹). - **CALCULATE THE ANGLE:** Substitute the known ratio into the chosen inverse function to obtain the size of the angle. ## EXAMPLE: Assume we have a right-angled triangle with a hypotenuse of length 10 units and the side opposite angle α has a length of 6 units. Let's calculate the angle α. - **CHOOSE THE TRIGONOMETRIC FUNCTION:** Since we know the hypotenuse and the side opposite angle α, we use sine: sin α = opposite side / hypotenuse = 6 / 10 = 0.6. - **USE THE INVERSE FUNCTION:** α = arcsin(0.6) (or α = sin⁻¹(0.6)). - **CALCULATE THE ANGLE:** Use a calculator or a table of values to calculate arcsin(0.6), which gives an approximate value for the angle α. (Using a calculator, α ≈ 36.87° or ≈ 0.6435 radians).