Right triangle: A triangle in which one angle is a right angle
Trigonometric functions on a circle with radius r:
For any angle in standard position, let be the point on the terminal side of that is also on the circle .
,, , , , and .
The trigonometric functions of an acute angle:
If is an acute angle of a right triangle, the six trigonometric functions of are as follow:
, , , , , and .
Two angles are called complementary if their sum equals to 90 degrees.
Angle of elevation:
The acute angle measured from the horizontal to a line-of-sight observation of the object.
Angle of depression:
The acute angle made by the line-of –sight observation of the object and the horizontal.
The trigonometric functions of any angle:
Let be an angle in standard position and let P(x,y) be a point, not the origin, on the terminal side that can be in any quadrant. If is the distance from the origin to the point P(x,y), then
, , , , , and
, , , and .