Everything Trig and Geomtry

Arc Length

The distance along the curve of a circle between two points.

Sector Area

The area enclosed by two radii of a circle and the arc between them.

Central Angle

The angle formed at the center of a circle by two radii.

Tangent Line

A line that touches a circle at exactly one point and is perpendicular to the radius at that point.

Inscribed Angle

An angle formed by two chords in a circle which have a common endpoint.

Circumference

The total distance around the circle, calculated by the formula C = 2πr.

Formula for Circular Sector Area

Area = (Central Angle/360) * πr².

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Circle Radius

A line segment that extends from the center of the circle to any point on the circle.

Similar Triangles

Triangles that have the same shape but may differ in size; corresponding angles are equal and corresponding sides are proportional.

Congruent Triangles

Triangles that are identical in shape and size; corresponding sides and angles are equal.

Area of a Circle

A = πr² where r is the radius of the circle.

Volume of a Cylinder

V = πr²h where r is the radius and h is the height of the cylinder.

Proportional Sides in Similar Triangles

If two triangles are similar, the ratio of the lengths of corresponding sides is constant.

Pythagorean Theorem

In a right triangle, a² + b² = c², where c is the hypotenuse.

Isosceles Triangle

A triangle with at least two sides of equal length.