What is the formula for tan? For example tan N. Is it the opposite angle/hypotneuse? What about sin and cosine?

1. An idea for an invention

2. Record companies lose money
3. The Internet can make it easier

Trust Me

tan x= (opposite side length)/(adjacent perendicular side length)

= sin x/cos x

sin x = (opposite side length)/(hypotenuse)
= x - x^3/3! + x^5/5! -...
(if x is in radians)

cos x = (adjacent perpendicular side length)/(hypotenuse)
= 1 - x^2/2! + x^4/4! - ...
(if x is in radians)

This provides both the right-triangle definitions and the infinite series representations of those trigonometric functions

The tangent function (tan) is a trigonometric function that relates the ratio of the opposite side to the adjacent side of a right triangle. It is commonly used to find the value of an angle (N) when the lengths of the sides of a right triangle are known.

The formula for tan N is defined as the opposite side divided by the adjacent side:

tan N = opposite side / adjacent side

In other words, if you have a right triangle, and you know the length of the opposite side and the length of the adjacent side to angle N, you can find the tangent of angle N by dividing the opposite side by the adjacent side.

However, it's important to note that the tangent function can also be used on any angle, not just within a right triangle. In this case, the tangent is defined as the y-coordinate divided by the x-coordinate of a point on the unit circle, where the radius is 1.

As for the sine (sin) and cosine (cos) functions, they are also trigonometric functions that relate the ratios of the sides of a right triangle. The sine function represents the ratio of the opposite side to the hypotenuse, while the cosine function represents the ratio of the adjacent side to the hypotenuse.

The formulas for sin N and cos N can be written as follows:

sin N = opposite side / hypotenuse
cos N = adjacent side / hypotenuse

Similar to tangent, these formulas apply specifically to right triangles. However, the sine and cosine functions can also be used with any angle, as they are defined based on coordinates on the unit circle.

To summarize:
- tan N = opposite side / adjacent side
- sin N = opposite side / hypotenuse
- cos N = adjacent side / hypotenuse

These functions are fundamental in trigonometry and are used in a wide range of fields, including physics, engineering, and mathematics.