# Mathematics - Trigonometry - Trigonometric Functions

How do you figure out trigonometric functions?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

How do you figure out trigonometric functions?

Sin, Cos and Tan functions

The trigonometric functions of angles are the ratios of the various sides of a triangle. Consider a right-angled triangle ABC as shown in the figure below.

The following terminology is useful.

â€¢ Hypotenuse: The side opposite to the right angle in a triangle is called the hypotenuse. Here the side AC is the hypotenuse.

â€¢ Opposite Side: The side opposite to the angle in consideration is called the opposite side. So, if we are considering angle A, then the opposite side is CB.

â€¢ Base: The third side of the triangle, which is one of the arms of the angle under consideration, is called the base. If A is the angle under consideration, then the side AB is the base.

For angle A (sometimes referred to as angle CAB), the following fundamental trigonometric functions can be defined.

Sine of A = sin A = Opposite Side / Hypotenuse = CB/CA = a/b

Cosine of A = cos A = Base / Hypotenuse = AB/CA = c/b

Tangent of A = tan A = Opposite Side / Base = CB/AB = a/c

From the definitions, it can be seen that tan A = sin A / cos A.

Cosec, Sec and Cot Functions

A few more useful functions can be defined.

Cosecant of A = cosec A = 1 / sin A = b/a

Secant of A = sec A = 1 / cos A = b/c

Cotangent of A = cot A = 1 / tan A = c/a

From the definitions, it can be seen that cot A = cosec A / sec A

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