Trignometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. The most commonly used trignometric functions are sine, cosine, and tangent.
Some common trignometric identities include the Pythagorean identities, double angle identities, and half angle identities. These identities can be used to simplify trignometric expressions and equations.
The unit circle is a circle with a radius of 1 centered at the origin on a coordinate plane. It is used to visualize trignometric functions and their values for different angles. The x-coordinate of a point on the unit circle corresponds to the cosine value for that angle, while the y-coordinate corresponds to the sine value.
Trignometric functions are used in various fields such as engineering, physics, and astronomy to calculate and predict the behavior of waves, vibrations, and oscillations. They are also used in navigation and in the analysis and design of structures.
A trignometric function takes an angle as input and gives a ratio of sides as output, while an inverse trignometric function takes a ratio as input and gives an angle as output. For example, the sine function takes an angle and returns the ratio of the side opposite the angle to the hypotenuse, while the inverse sine function takes a ratio and returns the angle whose sine is equal to that ratio.