The unit circle (or the trigonometric circle) is a circle of radius one centered at the origin of the Cartesian plane.

Sine and cosine are the two primary trigonometric functions. Given an oriented angle \theta, represented on the unit circle by a point P, the sine and cosine of \theta are defined respectively as the...

Tangent and cotangent are two trigonometric ratios derived from sine and cosine. Given an oriented angle \theta, the tangent is defined as the ratio of the sine of \theta to its cosine, and the...

Consider the unit circle centered at the origin \text{O} = ( 0 , 0 ) with radius 1.

The arcsine is the inverse of the sine function. Given a number x \in [ - 1 , 1 ] (i.e., the range of values the sine function can attain), arcsin ⁡ ( x

In the unit circle, the tangent of an angle \theta can be visualized as the length of the segment tangent to the circle at the point where the terminal side meets it, measured along the vertical...

We have seen that the sine of an angle can be introduced geometrically by looking at how a point moves along the unit circle.

The hyperbolic tangent and cotangent arise from the hyperbolic sine and cosine in exactly the same way that the circular tangent and cotangent arise from the circular sine and cosine.

A trigonometric identity is an equation involving trigonometric functions that holds for every admissible value of the variables.

The Pythagorean identity is an equation that connects trigonometry and geometry, and it derives directly from the Pythagorean theorem, which relates the sides of a right triangle.

Given an angle \theta in standard position on the unit circle, the acute angle formed between its terminal side and the horizontal axis is called the reference angle of \theta, and is usually denoted...

The law of sines states that in any triangle, the ratio between the length of a side and the sine of its opposite angle is the same for all three sides.

The law of cosines relates the sides of any triangle through the angle opposite to one of them. It can be viewed as a generalisation of the Pythagorean theorem, valid not only for right triangles but...