1. Rayat Shikshan Sanstha’s Hutatma Babu Genu Vidyalaya,Mahalunge Padwal
Std- 10 th
Sub-Geometry
Unit: Trigonometry
Presented By: Smt. Pokharkar V.M.

2. Definition
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

3. Sine function (sin), defined as the ratio of the side opposite the angle to thehypotenuse. Cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse. Tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. Many people find it easy to remember what sides of the right triangle are equal to sine, cosine, or tangent, by memorizing the word SOH-CAH-TOA (see below under Mnemonics).

4. The reciprocals of these functions are named the cosecant (csc or cosec), secant (sec), and cotangent (cot), respectively:

7. The Unit Circle The equations listed in the introduction are only defined for right triangles. However, the domain of the angles is all real numbers. Therefore, we need a unit circle to solve the trigonometric values. With the concept of unit circle, we can still use our definitions for the functions, except this time, allow negative values for both x and y.

8. Negative Angles Negative angles are defined by rotating clockwise from the x-axis. Basing on the unit circle, we can make the following conclusion about the signs of the functions in each quadrant:

9. Identities

10. Function
Abbreviation
Description
sine
sin
opposite / hypotenuse
cosine
cos
adjacent / hypotenuse
tangent
tan (or tg)
opposite / adjacent
cotangent
cot (or cotan or cotg or ctg or ctn)
adjacent / opposite
secant
sec
hypotenuse / adjacent
cosecant
csc (or cosec)
hypotenuse / opposite