What is tan u?

In trigonometry, tan u is a trigonometric function that gives the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. It is defined as the ratio of the sine of the angle u to the cosine of the angle u, or:

$$tan u = \frac{sin u}{cos u}$$

The tan function is periodic with a period of π, meaning that it repeats itself every π units. The range of the tan function is all real numbers.

Properties of tan u

tan u is an odd function, meaning that it is symmetric about the origin.
tan u is not defined at u = (2n + 1)π/2, where n is an integer.
tan u has a maximum value of 1 and a minimum value of -1.

Identities involving tan u

tan u = cot u
tan u = sec u – 1
tan u = csc u – 1

Applications of tan u

tan u is used in surveying to measure the height of objects and the distance between objects.
tan u is used in navigation to find the direction of travel.
tan u is used in engineering to calculate the angle of a slope.

Conclusion

The tan function is a versatile trigonometric function that has many applications in science, engineering, and navigation. By understanding the definition, properties, and identities of the tan function, you can use it to solve a variety of trigonometric problems.

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