Trigonometry – Cosine function (cos)

C-A-H

The cosine function of an angle is a trigonometric function that tells us about the relationship between that angle and the sides of a right triangle. It’s often written as “cos(θ),” with θ representing the angle.

Here’s a simple way to understand it:

1. Imagine a right triangle, which is a triangle with one 90-degree angle (a square corner).
2. The cosine of an angle θ (measured in degrees or radians) is found by looking at the ratio of the length of the side adjacent to θ to the length of the hypotenuse.
3. The “adjacent side” is the one that’s next to the angle θ but not the side you’re measuring the angle from.
4. The “hypotenuse” is the longest side of the right triangle, opposite the right angle.

Cos(θ) = (length of adjacent side) / (length of hypotenuse)

When θ is 0 degrees or 0 radians, the adjacent side is the same length as the hypotenuse, so cos(θ) is 1. When θ is 90 degrees or π/2 radians, the adjacent side has no length, so cos(θ) is 0. As θ increases, cos(θ) decreases and goes towards -1 when θ is 180 degrees or π radians. It keeps oscillating between -1 and 1 as θ varies.

In simpler terms, the cosine function helps us understand how wide or narrow the angle is within a right triangle by comparing the side next to the angle to the longest side.

Or try to imagine it this way…

Think of the cosine like a merry-go-round. Imagine you’re sitting on a horse that starts right at the top, and as the merry-go-round goes around, a horse goes up and down.

Now, the cosine function helps to figure out how high or low a horse is at any moment. When it is at the very top, the cosine is 1, because it is as high as it can be. As it go down, the cosine gets smaller and smaller.

When it is down at the very bottom, the cosine is -1 because it is as low as it can go. Then, as it start going back up, the cosine goes up too. It keeps going up and down just like the horse on the merry-go-round.

Now, the difference between sine and cosine can be explained like this:

1. For the sine function, at 0 degrees (or 0 radians), you start at the middle (neither up nor down), and the sine is 0. As you go around the merry-go-round, you move up and down, and the sine goes from 0 to 1 and back to 0 as you complete half of the circle.

1. For the cosine function, at 0 degrees (or 0 radians), you start at the highest point, and the cosine is 1. As you go around the merry-go-round, you move up and down, and the cosine goes from 1 to 0 and then to -1 as you complete half of the circle.

So, the difference lies in the starting point and the initial values, but both functions share the property of oscillating between -1 and 1 as you go around the circle.