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.

Numerator : The numerator of a fraction $\frac{a}{b}$ is the number $a$ above the fraction bar.

Quotient : A quotient is the result of a division.

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 $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$

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.

Isosceles triangle : An isosceles triangle is a triangle in which two side length are the same. The two angles at which these two sides meet the third side are the same.

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.

Pi : Pi or $\pi$ is an irrational number approximately equal to 3.14 that is defined as the quotient of the circumference and the diameter of a circle.

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.

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 $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$

Adjacent : Adjacent means next to each other.

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.

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 $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$

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 $\arctan x.$