Trigonometric Functions Table

Trigonometric Functions Table

Function Right Triangle Definition Unit Circle Definition

Sine Length of the side opposite angle Ө/ length of the hypotenuse y/radius of the circle, since this an unit circle the radius is 1, thus making it the y coordinate where the terminal side of the angle Ө intersect the unit circle

Cosine Length of the side adjacent angle Ө/ length of the hypotenuse x/radius of the circle, since this an unit circle the radius is 1, thus making it the x coordinate where the terminal side of the angle Ө intersects the unit circle

Tangent Length of the side opposite angle Ө/ length of side adjacent angle Ө sin Ө/cos Ө, thus making it y/x where x≠0

Cosecant Length of hypotenuse/ length of side opposite angle Ө Radius/y, since this an unit circle the radius is 1, making it 1/y where y≠0

Secant Length of hypotenuse/ length of side adjacent angle Ө Radius/x, since this an unit circle the radius is 1, making it 1/x where x≠0

Cotangent Length of side adjacent angle Ө/ length of side opposite angle Ө cos Ө/ sin Ө, thus making it x/y where y≠0

The right triangle definition of the trigonometric function and the unit circle definition of said functions relate in so many different way. If you look figure 2(A2) you will see that within the unit circle there is a smaller picture of the triangle in figure 1(A1). In order to find the definition of the trigonometric functions in the unit circle you draw a right triangle with in the circle. Using the knowledge that a unit circles radius is 1; we can not only simplify, but also better understand the trigonometric functions. In figure 3(A3) I have shown an enlarged picture of the right angle from the unit circle shown in figure 2(A2), if you compare the right triangle from figure 1(A1) and figure 3(A3) you will see they are both right angle triangles. Knowing that they are both right angle triangles we can use the right triangle definitions of the trigonometric functions and apply that understanding to the...