4.1 Radian & Degree Measure

Trigonometry: Radian and Degree Measure

When the length of a segment of the circumference of a circle is equal to the radius, this is a measurement known as a radian. There are 2π radians in a circle.


There are 2π radians in one full revolution. 2π radians = 360º

To convert degrees to radians, you multiply the degree by π/180

For example, take 45º 45 • π/180 = 45π/180 = π/4

45º is the same measurement as π/4 radians


You can look at a circle as either 360º or 2π radians. Because it is all proportional, π radians is the same as 180º, π/2 radians is the same as 90º, π/4 is the same as 45º, etc.




Cosine is the x coordinate of the endpoint and sine is the Y coordinate.

When two measurements land on the same line, these measurements are called co-terminal. For example, π/4 radians is the same as 9π/4 radians, and because of this, they are co-terminal.