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Knowledge Trigonometric Functions

Trigonometric ratio definition

Trigonometric Ratio means the ratio of the sides of the right triangle. To learn this subject, students need to Use prior knowledge of similar triangles as a basis for understanding. Studying well in trigonometry requires you to remember the definition of trigonometry. Middle school level used to define right triangles. The trigonometric ratio is the ratio of the two sides of a right triangle, which is called as follows.

“Sine A” The sine of angle A, abbreviated as sin A, is obtained from the ratio of the length of the hypotenuse A to the length of the hypotenuse.

“Cos A” The cosine of angle A or abbreviated cos A is found by the ratio of the length of the adjacent angle A to the length of the hypotenuse.

“Tangent A” The tangent of angle A, also abbreviated tan A, is obtained from the ratio of the length of the opposite side of angle A to the length of the adjacent side of angle A.

The cosec, sec, and cot functions are also used to define them. This is the reciprocal of sin, cos, and tan, respectively, so you need to remember the sin, cos, tan function , and you automatically get the cosec, sec and cot parts .

“Cotangent A” The cotangent of angle A, also abbreviated as cot A, is obtained from the ratio of the length of the adjacent side A to the length of the hypotenuse A.

“Secant A”, the secant of angle A, also abbreviated as sec A, is obtained from the ratio of the hypotenuse to the length of the adjacent side A.

“Cosecant A,” the cosecant of angle A, abbreviated cosec A, is obtained from the ratio of the hypotenuse to the hypotenuse of angle A.


To define a trigonometric function for angle A, we define that any of the angles in a right triangle be angle A.
Name each side of the triangle as follows.

The hypotenuse is the side that is the hypotenuse. Or the longest side of a right triangle, here is h.
The opposite side is the opposite side. The angle we are interested in here is a.
The adjacent side is the side adjacent to the angle that We care, and the right angle here is b.

Will get

1). The sine of the angle is the ratio of the length of the opposite side To the length of the hypotenuse, here is

sin (A) = cross /
square = a / h

2). The cosine of the angle is the ratio of the length of the adjacent side. To the length of the hypotenuse, here is

cos (A) = align / right = b / h

3). The tangent of the angle is the ratio of the length of the opposite side. Per adjacent side length, here is

tan (A) = cross / align = a / b

4). The cosecant csc (A) is the multiplicative inverse function of sin (A), that is, the ratio of the hypotenuse length. Per side length

csc (A) = square / cross = h / a

5). The secant sec (A) is the multiplicative inverse function of cos (A), that is, the ratio of the hypotenuse length. Per side length

sec (A) = square / align = h / b

6). The cotangent cot (A) is the multiplicative inverse function of tan (A), that is, the ratio of the adjacent side lengths. Per side length

cot (A) = align / skip = b / a

A simple way to remember
how to remember is to remember, cross-aligned, cross-aligned, which means

Across the orthogonal … sin = opposite / hypotenuse,
justified … cos = adjacent / hypotenuse, just
opposite … tan = opposite / adjacent

NOTE
A right triangle has a 90 ° angle (π / 2 radians), herein C , angles A and B are variable. Trigonometric functions define the relationship between side lengths and internal angles of a triangle. Right angle

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