What are sin and cos and why are they used so frequently in math?
In: 6
Imagine a circle.
All circles are the same shape, so it doesn’t matter how big, but to ensure we are on the same page, let’s say it is a circle with a radius of 1. “A unit circle ”
Imagine a dot travelling around the edge of the circle. It moves at a steady pace. Do you see it?
Okay, now, you see how that point goes up and down over and over? Let’s track that movement. Ignore the side to side movement, just focus on vertical distance from the centre of the circle.
The dot has to start somewhere, so let’s say it starts off to the far right and we’ll let it move anticlockwise.
So the height will be 0, 1, 0, -1, 0, 1, 0, -1 as it travels around. With many values in between.
This graph is called sine. We shorten it to sin often.
If you track side to side movement inatead you end up with the same pattern (a circle is the symmetric after all), but because we start of the far right, you will start with 1, 0, -1, 0, 1, 0, -1, 0. This is COsine. We often shorten it to cos.
I’d encourage you to Google image search for “unit circle trigonometry gif”. It will show you what I described in motion.
Latest Answers