A function of an angle expressed as the ratio of two of the sides of a right-angled triangle containing that angle is called the trigonometric function. For example f(θ) = sin (θ), g(θ) = cos (2θ), h(α) = tan(α) + 5, etc.
In another word, a function containing trigonometric ratio as an independent variable is called a trigonometric function. Trigonometric functions are also elementary functions. Trigonometric functions include six basic functions
- Sine, a.k.a sin(θ)
- Cosine, a.k.a cos(θ)
- tangent, a.k.a tan(θ)
- cotangent, a.k.a cot(θ)
- secant, a.k.a sec(θ)
- cosent, a.k.a cos(θ)
Each of these trigonometric functions has its own inverse trigonometric function.
The trigonometric function can be defined using the unit circle as shown in the figure below.
The figure above shows radius r = 1. Let M (x,y) be the point in the circle and the angle made by OM on X-axis be α.
The sine of an angle α is the ratio of the y-coordinate of the point M(x,y) to the radius r. ie, sin α = y/r. Since r is 1, the sine is equal to the y-coordinate of the point M(x,y)
The cosine of an angle α is the ratio of the x-coordinate of the point M(x,y) to the radius r. So, cos α = x/r. Since r is 1, the
Similarly tan α = y/x where x ≠ 0.
cot α = x/y where y ≠ 0
sec α = r/x where x ≠ 0
cosec α = r/y where y ≠ 0