Solution of Index Triangles

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Algebra

Expressions: Algebraic expressions are formed from variables and constants using arithmetic operations. E.g. 2x + 3y.
Equations: An equation is a statement that equates two algebraic expressions. E.g. 2x -5 = 10y.
Solving Equations: Solving an equation involves finding the values of the variables that make the equation true.
Inequalities: An inequality compares two expressions and includes >, <, >= or <=.
Solving Inequalities: Similar to solving equations, but the solution is usually a range of values.

Definition: Algebraic fractions have variables in the numerator, the denominator, or both. E.g. (2x+3)/(x-1).
Simplifying Algebraic Fractions: This involves factorising both the numerator and the denominator and then cancelling common factors.
Adding and Subtracting Algebraic Fractions: To add or subtract algebraic fractions, you need a common denominator.
Multiplying and Dividing Algebraic Fractions: Algebraic fractions can be multiplied or divided similarly to numerical fractions.

Definition: Completing the square is a method used to solve quadratic equations, rewrite quadratic functions, and evaluate integrals.
Steps to Complete the Square: To complete the square, the quadratic equation is rearranged into the form (x-h)² = k.
Applications: Completing the square helps us solve quadratic equations, graph quadratic functions, and find the minimum or maximum value of a function.

Linear Equations: Linear equations are equations of first degree. They graph a straight line when plotted on a graph.
Quadratic Equations: Quadratic equations are of second degree and the highest exponent of the variable is 2.
Polynomial Equations: Polynomial equations are expressions with more than two algebraic terms.
Simultaneous Equations: Simultaneous equations are a set of equations that are solved together.

Trigonometric Ratios: These are ratios of the sides of a right triangle and include sine, cosine, and tangent.
Unit Circle: The unit circle connects trigonometry with geometry.
Trigonometric identities: These are equalities that involve trigonometric functions and hold true for all values of the occurring variables.

Definition: Trigonometric equations are equations that involve trigonometric functions.
Solving Trigonometric Equations: These are solved using algebraic methods and trigonometric identities.
Periodicity of Trigonometric Functions: The concept of periodicity is vital in solving trig functions.

Sine, Cosine, and Tangent Rules: These rules help solve triangles, especially when they are not right-angled.