Take two perpendicular and graduated lines. Then draw a circle of radius 1 and whose center is the intersection of the lines. Now, draw a line passing through O ; the angle between this line and the horizontal axis is 40 °. Denote by M the intersection of this line and the circle. The abscissa of M is cos(40) and its ordinate is sin(40). The angle you chose doesn't matter : M is on the circle, you'll always obtain : When you move M to the right, its cosine gets closer to 1 and its sine gets closer to 0 ; when it goes up, its cosine gets closer to zero and its sine gets closer to 1. Sine et Cosine are functions : give them angles (degrees or radians), they will give you numbers between -1 and 1 in return. The radianThe radian is a unit of angular measurement. If the length of the red arc is x, then the angle measures x radians.The whole circle measures 360 degrees. In radians, it measures the circumference of the circle, that is 2 (the radius of the circle is still 1). In the drawing, the angle x is approximately 1 radian. As you know that 2 rad=360°, you can convert, thanks to a cross-product, degrees into radians and radians into degrees. Hence : Table of values : sine and cosineYou have to know by heart the cosine and sine values of the angles below (to learn them, you can learn the drawing).
GraphIf angles are greater than 2, the point M turns around the circle ; when it is 2 radians, it comes back to the same place. Hence :For example , so you can draw, thanks to the table of values, the graph of the cosine function, and the graph of the sine function : You can prolong the two graphs infinitely. On the graph, we can see than cosine is even (symmetric with respect to the Y-axis ), and the sine is odd (symmetric with respect to the origin). TangentWe won't say much about the tangent function on this page. Nevertheless, you have to know that :See also : trigonometry on fmaths.com |