Sine and cosine are written using functional notation with the abbreviations sin and cos.
Often, … See more

To define the sine and cosine of an acute angle α, start with a right triangle that contains an angle of measure α; in the accompanying figure, angle α in triangle ABC is the angle of interest. The three sides of th… See more

Exact identities (using radians):
These apply for all values of .
The reciprocal of sine is cosecant, i.e., the reciprocal of is . Cosecant gives the ratio of the length of the hypotenuse to the length of the oppo… See more

Zero is the only real fixed point of the sine function; in other words the only intersection of the sine function and the identity function is . The only real fixed point of the cosine function is called the Dottie number. … See more

The law of sines states that for an arbitrary triangle with sides a, b, and c and angles opposite those sides A, B and C:
This is equivalent to the equality of the first three expressions below:
where R is … See more

Sine and cosine are used to connect the real and imaginary parts of a complex number with its polar coordinates (r, φ):
The real and imaginary parts are:
where r and φ represent the magnitude and angle of th… See more