The six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. These functions are used to relate the angles of a right triangle to the lengths of its sides.
Trigonometric functions are used in a variety of fields, such as engineering, physics, and astronomy. They are used to calculate distances, heights, and angles in real-world scenarios. For example, they are used in navigation systems, building construction, and satellite imaging.
The unit circle is a circle with a radius of 1 unit. It is used to understand and visualize the relationships between the trigonometric functions and angles. The x-coordinate of a point on the unit circle represents the cosine of the corresponding angle, while the y-coordinate represents the sine. The unit circle also helps in understanding the periodic nature of trigonometric functions.
Sine and cosine are both trigonometric functions, but they differ in their definitions. Sine is the ratio of the opposite side of a right triangle to its hypotenuse, while cosine is the ratio of the adjacent side to the hypotenuse. In other words, sine is the y-coordinate on the unit circle, while cosine is the x-coordinate.
Trigonometric functions are primarily used to relate the angles and sides of a right triangle. The sine, cosine, and tangent functions are ratios of the sides of a triangle, while the other three functions (cotangent, secant, and cosecant) are reciprocals of these ratios. These functions are used to solve for missing sides or angles in a triangle.