Trigonometric functions of an acute angle
Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle. There are six basic trigonometric functions, which are tabulated here along with equations relating them to one another
Sine: The sine of an angle in a right triangle equals the opposite side divided by the hypotenuse.
Cosine: The cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse.
Tangent: The tangent is the opposite side divided by the adjacent side.
Cosecant (csc): is the reciprocal of sine, i.e. the ratio of the length of the hypotenuse to the length of the opposite side.
Secant (sec): is the reciprocal of cosine, i.e. the ratio of the length of the hypotenuse to the length of the adjacent side.
Cotangent (cot): is the reciprocal of tan, i.e. the ratio of the length of the adjacent side to the length of the opposite side.
| sin A |
= |
opposite
hypotenuse |
= |
a
c |
|
csc A |
= |
hypotenuse
opposite |
= |
c
a |
| |
| cos A |
= |
adjacent
hypotenus |
= |
b
c |
|
sec A |
= |
hypotenuse
adjacent |
= |
c
a |
| |
|
tan A
|
= |
opposite
adjacent |
= |
a
b |
|
cot A
|
= |
adjacent
opposite |
= |
b
a |
|
|
