Given a right-triangle (a triangle with a right angle) with acute angle α, the cosine of α is the value of the ratio: $ \cos(\alpha)=\large{\frac{\text{side adjacent}\,\, \alpha}{\text{hypotenuse}}}=\large{\frac{\text{adj}}{\text{hyp}}} $

Click and drag the angle α to any value between 0° and 90°.

Then click and drag b and b' to make any 2 right-triangles you want with angle α.

Look at first triangle: Divide the length of the side adjacent to the angle α by the length of the hypotenuse. Write this number down.

Look at the second triangle and again divide the lenth of the side adjacent to the angle α by the length of the hypotenuse. It should be the same number!

This is the value of cos(α).

y=cos(x) & Unit Circle - Degrees Directions and Links

Click and drag the slider for α. Note the size of α in degrees and in radians. (Although we wrote the word radians, it should NOT be written. There is no unit with radians.)

The ANGLE α is on the x-axis. The ANGLE α is the LENGTH OF THE ARC in the unit circle for the angle α in degrees. Read this sentence until you understand it. It is critical.

The x-coordinate of the point T ((width of the triangle) is the value of the cosine function of the angle α.

Definition of Cosine Directions and Links

coskey and the size of the angle α orCosine - Nested Triangles Directions and Links

y=cos(x) & Unit Circle - Degrees Directions and Linksy=cos(x) & Unit Circle - Radians Directions and Links