Summary
Highlights
Trigonometry is introduced as a powerful method to determine unknown lengths and angles in triangles. It becomes essential when only one side and an angle are known, unlike the Pythagorean theorem which requires two sides.
Ancient Greek mathematicians discovered specific ratios in 90-degree triangles. These foundational ratios were named sine (sin), cosine (cos), and tangent (tan). The video will explore each of these in subsequent discussions.
The sine of an angle (e.g., sine of angle theta) is defined as the ratio of the length of the side opposite to that angle divided by the length of the hypotenuse. The hypotenuse is always the longest side and is opposite the 90-degree angle.
Several examples are provided to illustrate how to apply the sine ratio. For different angles in right-angled triangles, the sine is calculated by identifying the opposite side and the hypotenuse. For instance, if an angle's opposite side is 3 and the hypotenuse is 5, the sine of that angle is 3/5.
The video concludes by reiterating the core definition of sine: it is always the length of the opposite side divided by the length of the hypotenuse.