Explore BrainMass

# Mathematics - Trigonometry - Trigonometric Functions

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

How do you figure out trigonometric functions?

https://brainmass.com/math/trigonometry/mathematics-trigonometry-trigonometric-functions-222158

## 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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!