Why do we use radians instead of degrees in trigonometry?

Radians make it possible to relate a linear measure and an angle measure. The length of the arc subtended by the central angle becomes the radian measure of the angle. This keeps all the important numbers like the sine and cosine of the central angle, on the same scale.

Why are radians not degrees?

Degrees measure angles by how far we tilted our heads. Radians measure angles by distance traveled. or angle in radians (theta) is arc length (s) divided by radius (r). A circle has 360 degrees or 2pi radians — going all the way around is 2 * pi * r / r.

Why do trig functions have a domain of all real numbers?

As we understand, the sin(x) is defined as the opposite divided by the hypotenuse. For this unit circle, at any point, sin(x) is equal to opposite / 1. This measure of opposite can be defined for all the points on the circle, indicating that the angle x can take any value. So, the domain of sin(x) is all real numbers.

What is the domain of trigonometric functions?

The domain and range of trigonometric functions are given by the angle θ and the resultant value, respectively. The domain of the trigonometric functions are angles in degrees or radians and the range is a real number.

What is the advantage of using radians?

The biggest advantage offered by radians is that they are the natural measure for dividing a circle. If you take the radius of a given circle and bend it into an arc that lies on the circumference, you would need just over six of them to go completely around the circle. This is a fact that is true for ALL circles.

Why are radians used in calculus?

Radians make it possible to relate a linear measure and an angle measure. A unit circle is a circle whose radius is one unit. The one unit radius is the same as one unit along the circumference.

Which trigonometric functions have a period of π?

The functions sin x, cos x, csc x, and sec x all have the same period: 2π radians. The graphs of y = tan x and y = cot x repeat every 2π radians but they also repeat every π radians. Thus, the functions tan x and cot x have a period of π radians.