Measuring an Angle

Angles are a fundamental concept in geometry and trigonometry. Angles are typically measured in degrees or radians. The measure of an angle is the amount of rotation from the initial ray to the terminal ray. Radians are often preferred in mathematical and scientific applications because they have a more direct relationship with other trigonometric functions and because they are “unitless” measures. Angles can be measured using a protractor, a tool with a semicircular scale marked in degrees. Alternatively, angles can be measured using a compass and straightedge constructions. Trigonometric functions capture fundamental relationships between the sides and angles of a right triangle. The three primary trigonometric functions are sine, cosine, and tangent. The chapter defines the three primary trigonometric functions of an acute angle of a right triangle. A mathematical identity is an equation that holds true for any value of the variables involved in the equation.