Sign In
Trigonometric functions are functions that relate an input, which represents an acute angle of a right triangle, to a trigonometric ratio of two of the triangle's side lengths. The angle is usually measured in radians.
Trigonometric functions are also defined for angles θ that are not acute by using the appropriate reference angle θ'.
For input values that are not between 0 and 2π, the value of the coterminal angle that belongs to this interval is used instead. Therefore, trigonometric functions are periodic functions. The cosine and sine functions are defined by pairing the measure of the angle in standard position with the x- and y-coordinates of the intersection of the unit circle and the angle's terminal side, respectively.
Because of their close relation with the unit circle, trigonometric functions are also called circular functions. The domain of the sine and cosine functions is the set of all real numbers. Their range is the interval that goes from -1 to 1.
| Trigonometric Function | Domain | Range |
|---|---|---|
| y=sinx | All real numbers | [-1,1] |
| y=cosx | All real numbers | [-1,1] |
The tangent, cotangent, secant, and cosecant functions are defined as rational functions that involve the sine and cosine functions. The domain of each function does not include values that would make their denominator zero.
| Trigonometric Function | Ratio | Domain | Range |
|---|---|---|---|
| y=tanx | tanx=sinx/cosx | Real numbers except odd multiples of π2 | All real numbers |
| y=cotx | cotx=cosx/sinx | Real numbers except multiples of π | All real numbers |
| y=secx | secx=1/cosx | Real numbers except odd multiples of π2 | (- ∞, -1]⋃[1,∞) |
| y=cscx | cscx=1/sinx | Real numbers except multiples of π | (- ∞, -1]⋃[1,∞) |