Trigonometric Ratios and Laws Review

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: $$\frac{a}{\text{sin } A} = \frac{b}{\text{sin } B} = \frac{c}{\text{sin } C}$$ .

Cosine (Cos) is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is expressed as: $$\text{Cos } A = \frac{\text{Adjacent}}{\text{Hypotenuse}}$$ .

Sine (Sin) is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. It is expressed as: $$\text{Sin } A = \frac{\text{Opposite}}{\text{Hypotenuse}}$$ .

Tangent (Tan) is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is expressed as: $$\text{Tan } A = \frac{\text{Opposite}}{\text{Adjacent}}$$ .

A Regular Polygon is a figure where all sides and all interior angles are equal.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. It is expressed as: $$a^2 + b^2 = c^2$$ .

In any triangle, the larger the angle, the longer the side opposite that angle. This is known as the triangle inequality theorem.

The area of a triangle can be calculated using the formula: $$\text{Area} = \frac{1}{2}ab\text{sin } C$$ , where a and b are the lengths of two sides and C is the included angle.

Cotangent (Cot) is the reciprocal of the tangent function. It is defined as: $$\text{Cot } A = \frac{1}{\text{Tan } A} = \frac{\text{Adjacent}}{\text{Opposite}}$$ .

Sine and cosine are related through the identity: $$\text{sin}^2 A + \text{cos}^2 A = 1$$ .