The unit circle shows you all the angles from 0° to 360°. You can also refer to angles as segments of the unit circle circumference from 0 to 2π radians. If you imagine sweeping angles around the unit circle like a radar screen, it makes a series of triangles. The hypotenuse is (depending on how you look at it) either the longest side in the triangle or the radius of the unit circle.

A sine wave is what you get if you plot the triangle’s opposite side versus the angle. Sine waves are important in science and engineering, but also in music. When you’re playing a guitar the frets are all placed where they are to make certain sine waves. Light is a sine wave. Waves are sine waves. The motions of springs are sine waves. It goes on and on!

visualizingmath:


math-is-beautiful:


fourcylinder:


your friend. your enemy. your savior.


This is an extremely useful diagram. Angles in degrees and radians, and their cosines and sines.


This is actually the kind of stuff I should be posting. Fractals are cool, but this is helpful.



The Clear Science staff is going to take a crack at convincing everyone this figure is an essential and beautiful component of everything. And by everything we mean not only science, engineering, and math but also art, music, nature, and pretty much anything else.

visualizingmath:

math-is-beautiful:

fourcylinder:

your friend. your enemy. your savior.

This is an extremely useful diagram. Angles in degrees and radians, and their cosines and sines.

This is actually the kind of stuff I should be posting. Fractals are cool, but this is helpful.

The Clear Science staff is going to take a crack at convincing everyone this figure is an essential and beautiful component of everything. And by everything we mean not only science, engineering, and math but also art, music, nature, and pretty much anything else.

(Source: nxte)

tanya77:

Trig LOL

Okay the Clear Science Staff thinks this is funny. Get it?

tanya77:

Trig LOL

Okay the Clear Science Staff thinks this is funny. Get it?

(Source: christinanotchris)


Notice when we drew the velocity vector for our Smart Car, we also put in two smaller arrows. These arrows point exclusively in the x and y directions, and are the x and y components of the velocity vector. These components make a triangle with the velocity vector, which is the hypotenuse.
The mathematical study of triangles is called trigonometry, and one thing trigonometry is useful for is working with vectors. Even if you don’t know trigonometry, you’ve probably messed with the SIN, COS, and TAN buttons on a calculator. We can use the definition of a cosine (COS) to find the length of the x-component. On a calculator, type in 30, hit COS, and multiply that number by the hypotenuse (45 mph). You find that in the x direction only, the car is moving 39 mph.

Notice when we drew the velocity vector for our Smart Car, we also put in two smaller arrows. These arrows point exclusively in the x and y directions, and are the x and y components of the velocity vector. These components make a triangle with the velocity vector, which is the hypotenuse.

The mathematical study of triangles is called trigonometry, and one thing trigonometry is useful for is working with vectors. Even if you don’t know trigonometry, you’ve probably messed with the SIN, COS, and TAN buttons on a calculator. We can use the definition of a cosine (COS) to find the length of the x-component. On a calculator, type in 30, hit COS, and multiply that number by the hypotenuse (45 mph). You find that in the x direction only, the car is moving 39 mph.