The hypotenuse is the longest side of a right triangle, opposite the right angle. It is used in various trigonometric functions such as sine and cosine.
congrats on reading the definition of hypotenuse. now let's actually learn it.
The Pythagorean theorem states that $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
In a unit circle, the hypotenuse corresponds to the radius, which is always 1.
Sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse: $\sin(\theta) = \frac{opposite}{hypotenuse}$.
Cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{adjacent}{hypotenuse}$.
The hypotenuse can never be shorter than either of the other two sides in a right triangle.
Review Questions
What is the relationship between sine and cosine functions and the hypotenuse?
How does the Pythagorean theorem relate to finding the hypotenuse?
In a unit circle, what does the hypotenuse represent?
A fundamental relation in Euclidean geometry among the three sides of a right triangle: $a^2 + b^2 = c^2$.
Sine: A trigonometric function representing the ratio of the length of the opposite side to that of the hypotenuse: $\sin(\theta) = \frac{opposite}{hypotenuse}$.
Cosine: A trigonometric function representing the ratio of the length of the adjacent side to that of the hypotenuse: $\cos(\theta) = \frac{adjacent}{hypotenuse}$.