{"type":"video","version":"1.0","width":1920,"height":1080,"title":"Hello everyone. - Animated Video By Sarwan Rathor - Mango Animate","description":"Hello everyone. animation video uploaded by Sarwan Rathor. Trigonometric ratios are derived from right triangles, which are triangles with one 90-degree angle. These ratios help relate the angles of a triangle to the lengths of its sides. Here’s a simple explanation:### 1. **Right Triangle Basics**A right triangle has three sides:- **Hypotenuse:** The longest side, opposite the right angle.- **Adjacent Side:** The side next to the angle you’re focusing on, but not the hypotenuse.- **Opposite Side:** The side across from the angle you’re focusing on.### 2. **Trigonometric Ratios**There are three main trigonometric ratios: Sine, Cosine, and Tangent. These ratios are based on the relationships between the angles and the sides of the triangle.- **Sine (sin):** The sine of an angle is the ratio of the length of the opposite side to the hypotenuse.\\sin(\\theta) = \\frac{\\text{Opposite}}{\\text{Hypotenuse}}- **Cosine (cos):** The cosine of an angle is the ratio of the length of the adjacent side to the hypotenuse.\\cos(\\theta) = \\frac{\\text{Adjacent}}{\\text{Hypotenuse}}- **Tangent (tan):** The tangent of an angle is the ratio of the length of the opposite side to the adjacent side.\\tan(\\theta) = \\frac{\\text{Opposite}}{\\text{Adjacent}}### 3. **How These Ratios Are Derived**The trigonometric ratios are derived by examining different right triangles with the same angles but different side lengths. Make your animation and host online for free!","url":"https:\/\/mangoanimate.com\/w\/wb4egcqtwffclyy\/hello-everyone\/wcwegcqyjepcbt0\/","author_name":"Sarwan Rathor","author_url":"https:\/\/mangoanimate.com\/homepage\/1ef60d59-1e90-6850-9b7a-f23c915625cf","provider_name":"Mango Animate","provider_url":"https:\/\/mangoanimate.com","thumbnail_url":"https:\/\/online.mangoanimate.com\/ai\/w\/133425618837498688\/1\/thumb.jpg","thumbnail_width":1920,"thumbnail_height":1080,"html":"<iframe src=\"https:\/\/mangoanimate.com\/w\/wb4egcqtwffclyy\/hello-everyone\/wcwegcqyjepcbt0\/?type=embed\" width=\"840px\" height=\"473px\" frameborder=\"0\" scrolling=\"no\" webkitAllowFullScreen mozallowfullscreen allowFullScreen><\/iframe>"}