Circle : A circle is a two-dimensional shape. The boundary of a circle is a set of points that has the same distance (the radius) from the center of the circle.

Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Cot : In a right triangle with one of the angles adjacent to the hypotenuse being equal to $\alpha,$ $\cot \alpha$ is defined as the length of the leg adjacent to the angle divided by the length of the other leg. We have $\cot \alpha= \frac{1}{\tan \alpha} =\frac{\cos \alpha}{\sin \alpha}.$

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

Right triangle : A right triangle is a triangle that has a right angle. The sides that form the right angle are called legs, the third side is called hypotenuse. The area of a right triangle is half the product of the lengths of the two legs. The Pythagorean theorem is an important theorem for right triangles that allows to calculate the third side of a right triangle given the other two.

Sin : The sine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\sin \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the hypotenuse. For arbitrary angles the sine function can be extended in a periodic way by inscribing the right triangle in a circle. The sine can be used to calculate unknown side lengths in a triangle via the sine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Tan : The tangent of an angle $0\leq\alpha\leq 180^{\circ}$ or $\tan \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the leg adjacent to $\alpha.$ For arbitrary angles the tangent function can be extended in a periodic way by inscribing the right triangle in a circle. The tangent function can be used to calculate unknown side lengths and angles in right triangles via its definition. We have $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$

Tangent : A tangent is a line that touches a curve or a surface at one point without going through the curve or surface.

Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$

Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.

Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Cot : In a right triangle with one of the angles adjacent to the hypotenuse being equal to $\alpha,$ $\cot \alpha$ is defined as the length of the leg adjacent to the angle divided by the length of the other leg. We have $\cot \alpha= \frac{1}{\tan \alpha} =\frac{\cos \alpha}{\sin \alpha}.$

Hypotenuse : The hypotenuse in a right triangle is the side of the right triangle that does not have any endpoints at the corner with the right angle. The hypotenuse is the longest side in a right triangle and its length can be calculated from the other two side lengths using the Pythagorean theorem.

Leg of a right triangle : A leg of a right triangle is one of the two sides in a right triangle that form the right angle.

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

Quotient : A quotient is the result of a division.

Sin : The sine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\sin \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the hypotenuse. For arbitrary angles the sine function can be extended in a periodic way by inscribing the right triangle in a circle. The sine can be used to calculate unknown side lengths in a triangle via the sine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Tan : The tangent of an angle $0\leq\alpha\leq 180^{\circ}$ or $\tan \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the leg adjacent to $\alpha.$ For arbitrary angles the tangent function can be extended in a periodic way by inscribing the right triangle in a circle. The tangent function can be used to calculate unknown side lengths and angles in right triangles via its definition. We have $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$

Trigonometric function : Trigonometric functions are the functions commonly used in trigonometry like $\sin x,$ $\cos x,$ $\tan x,$ $\cot x$ and their inverse functions $\arcsin x,$ $\arccos x,$ and $\arctan x.$

Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.

Congruence : Two shapes are called congruent if they have the same shape and size. Two integers are called congruent modulo $x$ if they have the same remainder in a division by $x.$

Congruent triangle : Two triangles are called congruent if they have the same shape and size.

Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

Equilateral triangle : An equilateral triangle is a triangle with three sides of equal length. An equilateral triangle is also equiangular and has interior angles of $60^{\circ}.$

Half : A Half is the number equal to $\frac{1}{2}=0.5.$

Height : In a triangle a height (or altitude) is the shortest line segment that connects a side to its opposing corner. A height of a triangle is perpendicular to the side is started at. The three heights of a triangle intersect in a point, the so called orthocenter of the triangle. In a parallelogram the height is the shortest distance between two opposing sides. In a pyramid the height is the shortest distance between the base area and the corner of the pyramid that is not part of the base area. In a prism the height is the shortest distance between the two base faces.

Hypotenuse : The hypotenuse in a right triangle is the side of the right triangle that does not have any endpoints at the corner with the right angle. The hypotenuse is the longest side in a right triangle and its length can be calculated from the other two side lengths using the Pythagorean theorem.

Pythagorean theorem : The Pythagorean theorem states that in a right triangle the square of the hypotenuse $c^2$ equals the sum of the squares of the legs $a^2+b^2$. It can be used to calculate the length of a third side of a right triangle given the other two. It also can be used to calculate the lengths of diagonals in rectangles or cubes.

Right triangle : A right triangle is a triangle that has a right angle. The sides that form the right angle are called legs, the third side is called hypotenuse. The area of a right triangle is half the product of the lengths of the two legs. The Pythagorean theorem is an important theorem for right triangles that allows to calculate the third side of a right triangle given the other two.

Sin : The sine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\sin \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the hypotenuse. For arbitrary angles the sine function can be extended in a periodic way by inscribing the right triangle in a circle. The sine can be used to calculate unknown side lengths in a triangle via the sine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Square root : The square root of $x$ denoted by $\sqrt{x}$ is the positive number such that $(\sqrt{x})^2=\sqrt{x}\cdot \sqrt{x}=x.$ For example $\sqrt{9}=3.$

Square root of 2 : The square root of 2 also written as $\sqrt{2}$ is the positive number such that $(\sqrt{2})^2=\sqrt{2}\cdot \sqrt{2}=2.$ $\sqrt{2}$ is an irrational number and rounded to the nearest hundredths it is equal to 1.41.

Square root of 3 : The square root of 3 also written as $\sqrt{3}$ is the positive number such that $(\sqrt{3})^2=\sqrt{3}\cdot \sqrt{3}=3.$ $\sqrt{3}$ is an irrational number and rounded to the nearest hundredths it is equal to 1.73.

Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.

Third : A third either refers to the third object in an ordering or to the number $\frac{1}{3}=0.\overline{3}.$

Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$