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Tan 7pi/6 : Exact Value 1/√3 Explained
Tan 3pi/4 : Exact Value, −1, and How to Find It
Tan 2pi/3 : Exact Value, −√3, and How to Find It
Tan 2pi : Value, Unit Circle Proof, and Why It's 0
Tan 1 Degrees : Value 0.0175 and How to Find It
Tan 0 Degrees : Value, Proof, and Why It Equals 0
Sin Pi/6 : Exact Value 1/2 on the Unit Circle
Sin Pi/4 : Exact Value √2/2 Explained
Sin Pi/3 : Exact Value √3/2 on the Unit Circle
Sin Pi/2 : Exact Value on the Unit Circle (= 1)
Sin of Sin Inverse x : Value, Domain, and Examples
Sine Function : Graph, Period, Amplitude & Properties
Sin Double Angle Formula : Derivation, Identities, and Examples
Sin A Sin B Formula: Product-to-Sum Proof & Examples
Sin(a+b) Formula : Proof, Uses, and Examples
Sin A Cos B Formula : Derivation & Examples
Tan 7pi/6 : Exact Value 1/√3 Explained
Tan 3pi/4 : Exact Value, −1, and How to Find It
Tan 2pi/3 : Exact Value, −√3, and How to Find It
Tan 2pi : Value, Unit Circle Proof, and Why It's 0
Tan 1 Degrees : Value 0.0175 and How to Find It
Tan 0 Degrees : Value, Proof, and Why It Equals 0
Sin Pi/6 : Exact Value 1/2 on the Unit Circle
Sin Pi/4 : Exact Value √2/2 Explained
Sin Pi/3 : Exact Value √3/2 on the Unit Circle
Sin Pi/2 : Exact Value on the Unit Circle (= 1)
Sin of Sin Inverse x : Value, Domain, and Examples
Sine Function : Graph, Period, Amplitude & Properties
Sin Double Angle Formula : Derivation, Identities, and Examples
Sin A Sin B Formula: Product-to-Sum Proof & Examples
Sin(a+b) Formula : Proof, Uses, and Examples
Sin A Cos B Formula : Derivation & Examples
The goal was never to make kids faster at math — it was to make them fall in love with it. Speed is a byproduct of genuine understanding.
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Algebra
Variables, equations, and the language of math
Objective Function — Definition, Formula, and Examples
The objective function is the linear expression a linear programming problem sets out to maximize or minimize — usually written Z = ax + by, where x and y are decision variables. This article defines it, shows the Z = ax + by form, works six examples, and separates it clearly from the constraints.
Scalar Triple Product — Definition, Formula, Example
The scalar triple product of three vectors is a · (b × c), a single number equal to the signed volume of the parallelepiped built on those vectors. This article covers the definition, the determinant formula, six worked examples, why a zero result means the vectors are coplanar, and the mistakes to avoid
Square Root 1 to 25 — Values, Chart & Examples
The square root 1 to 25 chart gives √1 through √25, where five values (√1, √4, √9, √16, √25) are exact whole numbers and the other twenty are irrational, rounded here to three decimals. This article gives the full table, marks rational versus irrational, and shows how to read and rebuild it.
Geometry
Shapes, proofs, and spatial thinking
Vertex of a Parabola: Formula, How to Find, Examples
The vertex of a parabola is its turning point - the highest or lowest point on the curve - found from y = ax² + bx + c using x = -b/2a, then (h, k). This article covers the vertex formula, how to find it from standard, vertex, and intercept forms, six worked examples, and the sign mistake that flips the answer.
Vector Subtraction: Formula, Methods & Examples
Vector subtraction finds the difference of two vectors by adding the negative of the second: a - b = a + (-b). This article covers the component formula, the triangle and parallelogram methods, why subtraction is not commutative, the tip-to-tip direction of the result, and worked examples that turn the rule into a picture.
Vectors Triangle Inequality : Statement & Proof
The vectors triangle inequality states that for any two vectors, |a + b| ≤ |a| + |b| - the length of a sum never exceeds the sum of the lengths. This article states the full two-sided form, proves it two ways, pins down exactly when equality holds, and works six examples.
Trigonometry
Angles, waves, and circular harmony
Tan 7pi/6 : Exact Value 1/√3 Explained
The value of tan 7π/6 is exactly 1/(√3), or in rationalised form (√3)/3, which is about 0.5774. This article shows why the answer is positive (the angle lands in the third quadrant), how the reference angle (π)/6 produces the value, and how the unit circle confirms it, with a tangent table, worked examples, and the mistakes to sidestep.
Tan 3pi/4 : Exact Value, −1, and How to Find It
The value of tan 3pi/4 is exactly -1. This article works from the unit circle and the reference angle (π)/4, explains why the sign is negative in the second quadrant, gives a radian table, and works through examples plus common mistakes.
Tan 2pi/3 : Exact Value, −√3, and How to Find It
The value of tan 2pi/3 is exactly -√3, which is about -1.7321. This article works from the unit circle and the reference angle (π)/3, explains why the sign is negative in the second quadrant, gives a radian table, and works through examples plus common mistakes.
Parenting
Raising confident, curious young mathematicians
Math Formulas
Every essential formula, explained and derived
Maths Formulas for Class 10 — Chapter-Wise List
The maths formulas for class 10 span the full board syllabus — real numbers, polynomials, linear and quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry, circles, mensuration, statistics, and probability. This hub lists every formula by chapter, explains where each one comes from, and works one example per cluster so the formulas connect instead of floating loose.
nPr Formula — Permutations, Derivation, Examples
The nPr formula counts how many ordered arrangements of r objects you can make from n distinct objects: ⁿP r = (n!)/((n-r)!). This article derives that formula from the counting principle, defines every symbol, shows where order makes a permutation different from a combination, and works six examples from a simple line-up to a locked-position arrangement.
Sum of Arithmetic Sequence Formula — Proof, Examples
The sum of arithmetic sequence formula adds the first n terms of an arithmetic progression: Sₙ = n/2(2a + (n-1)d) = n/2(a + l). This article derives both forms by the pairing trick, defines every variable, works through six examples from one-step sums to finding n from a known total, and clears up the mistakes that cost the most marks.
Math Terms
Crystal-clear definitions with worked examples
CP Formula — How to Find Cost Price, Examples
The CP formula recovers the cost price of an item from its selling price and a profit or loss: CP = SP - profit, CP = SP + loss, and from a percentage, CP = 100/(100 + profit%) × SP or 100/(100 - loss%) × SP. This article derives all four forms, defines every term, and works six examples plus the percentage mistakes that flip answers.
Isosceles Triangle Formula — Area, Perimeter, Height
The isosceles triangle formula set is: area = 1/2bh (or b/2√(a² - (b²)/4) from the equal side a and base b), perimeter = 2a + b, and height = √(a² - (b²)/4). This article gives each formula, derives the height and area straight from the Pythagorean theorem, works six examples from one-step to a word problem, and clears up the mistakes that cost the most marks.
What Is a Chord? Definition, Properties & Examples
A chord is a straight line segment whose two endpoints both lie on a curve — most often a circle. This article defines the term, gives the chord-length formulas, lays out the key chord properties, works six examples, and clears up the chord-versus-diameter mix-up that trips students.
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