Question

What are the 6 trigonometric functions and their definitions?

Answer 1

There are six main trigonometric functions:

Sine (sin)

Cosine (cos)

Tangent (tan)

Secant (sec)

Cosecant (csc)

Cotangent (cot)

These functions are used to relate the angles of a triangle with the sides of that triangle. Trigonometric functions are important when studying triangles and modeling periodic phenomena such as waves, sound, and light.

To define these functions for the angle theta, begin with a right triangle. Each function relates the angle to two sides of a right triangle. First, let's define the sides of the triangle.





The hypotenuse is the side opposite the right angle. The hypotenuse is always the longest side of a right triangle.

The opposite side is the side opposite to the angle we are interested in, theta.

The adjacent side is the side having both the angles of interest (angle theta and the right angle).

The relationship between the trigonometric functions and the sides of the triangle are as follows:

sine(theta) = opposite / hypotenuse

cosecant(theta) = hypotenuse / opposite

cosine(theta) = adjacent / hypotenuse

secant(theta) = hypotenuse / adjacent

tangent(theta) = opposite / adjacent

cotangent(theta) = adjacent / opposite

Answer 2

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