"A figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle."
The measurement of the amount of turn between two lines or rays is called an angle.
Definitions: Basic definitions such as angle, degree, radian, and trigonometric functions (sine, cosine, and tangent).
Unit Circle: A circle with a radius of one, centered at the origin, used to explain the properties of trig functions.
Pythagorean identities: Basic trigonometric identities that relate sine, cosine, and tangent.
Trigonometric ratios: The ratios of the sides of a right-angled triangle to its angles.
Angle measures: Angles can be measured in degrees or radians, and these measurements are important to understand when working with trigonometric functions.
Trigonometric graphs: The graphs of sine, cosine, and tangent functions on the coordinate plane.
Trigonometric equations: Equations involving trigonometric functions and how to solve them.
Inverse trigonometric functions: The inverse functions of sine, cosine, and tangent.
Identities: Trig identities such as double angle formulas and the Pythagorean identities.
The law of sines: A formula that relates the side lengths and angles of a non-right triangle.
The law of cosines: A formula that relates the side lengths and angles of a non-right triangle.
Right triangle trigonometry: Using trigonometry to find the missing side lengths and angles of a right-angled triangle.
Applications of trigonometry: Real-world applications of trigonometry, such as in engineering, physics, and navigation.
Trigonometric series and Fourier analysis: Advanced topics that involve using trigonometric functions to represent complex functions.
Acute angle: An angle that measures less than 90 degrees.
Right angle: An angle that measures exactly 90 degrees.
Obtuse angle: An angle that measures more than 90 degrees but less than 180 degrees.
Straight angle: An angle that measures exactly 180 degrees.
Reflex angle: An angle that measures more than 180 degrees but less than 360 degrees.
Full angle: An angle that measures exactly 360 degrees.
Complementary angles: Two angles whose sum is 90 degrees.
Supplementary angles: Two angles whose sum is 180 degrees.
Adjacent angles: Two angles that share a common vertex and a common side.
Vertical angles: Two non-adjacent angles formed by the intersection of two lines.
Alternate interior angles: Angles that are on opposite sides of a transversal and inside the two lines, and are equal in measure.
Alternate exterior angles: Angles that are on opposite sides of a transversal and outside the two lines, and are equal in measure.
Corresponding angles: Angles that are in the same relative position at the intersection of two lines and are equal in measure.
Interior angles: Angles on the inside of a polygon formed by two adjacent sides.
Exterior angles: Angles on the outside of a polygon formed by extending one side of a polygon.
"The sides of the angle."
"The vertex of the angle."
"Plane angles."
"In the plane that contains the rays."
"Angles are also formed by the intersection of two planes; these are called dihedral angles. Two intersecting curves may also define an angle."
"Angles formed by the intersection of two planes."
"Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection."
"Angular measure or simply 'angle'."
"A measure defined as the ratio of a circular arc length to its radius."
"Yes, the angle of rotation may be a negative number."
"In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation."
"Angles formed by two rays are known as plane angles, while angles formed by intersecting curves may have different properties."
"No, angles formed by the intersection of two planes are known as dihedral angles."
"The magnitude of an angle refers to its measure, rather than its physical size."
"The paragraph does not explicitly mention the units in which angles are measured."
"Angles of rotation are a measure conventionally defined as the ratio of a circular arc length to its radius."
"No, an angle is formed specifically by two rays and shares a common vertex."
"The paragraph does not mention any restrictions on the orientation of the rays."
"Yes, angles formed by the intersection of two planes (dihedral angles) can exist in three-dimensional space."