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53 results for “sine”

Formulae (53)

Law of Sines

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Relates sides to opposite angles in any triangle.

Geometry & TrigonometryIntermediate

Law of Cosines

c^2 = a^2 + b^2 - 2ab\cos C

Generalizes Pythagoras to any triangle.

Geometry & TrigonometryIntermediate

Sine Double Angle

\sin(2\theta) = 2\sin\theta\cos\theta

Double-angle identity for sine.

Geometry & TrigonometryIntermediate

Cosine Double Angle

\cos(2\theta) = \cos^2\theta - \sin^2\theta

Double-angle identity for cosine.

Geometry & TrigonometryIntermediate

Tangent Identity

\tan\theta = \frac{\sin\theta}{\cos\theta}

Defines tangent in terms of sine and cosine.

Geometry & TrigonometryIntermediate

Sine Angle Sum

\sin(A \pm B) = \sin A\cos B \pm \cos A\sin B

Angle addition formula for sine.

Geometry & TrigonometryIntermediate

Cosine Angle Sum

\cos(A \pm B) = \cos A\cos B \mp \sin A\sin B

Angle addition formula for cosine.

Geometry & TrigonometryIntermediate

Cotangent Identity

\cot\theta = \frac{\cos\theta}{\sin\theta}

Cotangent as the ratio of cosine to sine.

Geometry & TrigonometryBasic

Cofunction Identity

\sin\theta = \cos(90\degree - \theta)

Sine and cosine of complementary angles are equal.

Geometry & TrigonometryBasic

Secant Definition

\sec\theta = \frac{1}{\cos\theta}

Reciprocal of cosine.

TrigonometryBasic

Sine Ratio (SOH)

\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}

Ratio of the side opposite an angle to the hypotenuse.

TrigonometryBasic

Cosine Ratio (CAH)

\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}

Ratio of the side adjacent to an angle to the hypotenuse.

TrigonometryIntermediate

Cosecant

\csc\theta = \frac{1}{\sin\theta}

Reciprocal of sine.

TrigonometryIntermediate

Secant

\sec\theta = \frac{1}{\cos\theta}

Reciprocal of cosine.

TrigonometryBasic

Tangent Identity

\tan\theta = \frac{\sin\theta}{\cos\theta}

Tangent equals sine divided by cosine.

TrigonometryIntermediate

Sine of a Sum

\sin(A+B) = \sin A\cos B + \cos A\sin B

Angle addition formula for sine.

TrigonometryIntermediate

Sine of a Difference

\sin(A-B) = \sin A\cos B - \cos A\sin B

Angle subtraction formula for sine.

TrigonometryIntermediate

Cosine of a Sum

\cos(A+B) = \cos A\cos B - \sin A\sin B

Angle addition formula for cosine.

TrigonometryIntermediate

Cosine of a Difference

\cos(A-B) = \cos A\cos B + \sin A\sin B

Angle subtraction formula for cosine.

TrigonometryIntermediate

Double Angle: Sine

\sin 2\theta = 2\sin\theta\cos\theta

Sine of twice an angle.

TrigonometryIntermediate

Double Angle: Cosine

\cos 2\theta = \cos^2\theta - \sin^2\theta

Cosine of twice an angle (also 2cos²θ−1 or 1−2sin²θ).

TrigonometryAdvanced

Half Angle: Sine

\sin\frac{\theta}{2} = \pm\sqrt{\frac{1-\cos\theta}{2}}

Sine of half an angle.

TrigonometryAdvanced

Half Angle: Cosine

\cos\frac{\theta}{2} = \pm\sqrt{\frac{1+\cos\theta}{2}}

Cosine of half an angle.

TrigonometryIntermediate

Law of Sines

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Relates sides of any triangle to the sines of opposite angles.

TrigonometryIntermediate

Law of Cosines

c^2 = a^2 + b^2 - 2ab\cos C

Generalises Pythagoras to any triangle.

TrigonometryIntermediate

Sinusoidal Function

y = A\sin(Bx + C) + D

General sine wave with amplitude A, period 2π/B, phase C, shift D.

CalculusIntermediate

Derivative of Sine

\frac{d}{dx}\sin x = \cos x

Derivative of the sine function.

CalculusIntermediate

Derivative of Cosine

\frac{d}{dx}\cos x = -\sin x

Derivative of the cosine function.

CalculusBasic

Derivative of Sine

\frac{d}{dx}\sin x = \cos x

The derivative of sine is cosine.

CalculusBasic

Derivative of Cosine

\frac{d}{dx}\cos x = -\sin x

The derivative of cosine is negative sine.

Data Science & MLIntermediate

Cosine Similarity

\cos\theta = \frac{A \cdot B}{\|A\|\|B\|}

Measures similarity between two vectors by the angle between them.

Finance & InterestIntermediate

Break-Even Point

Q = \frac{FC}{P - VC}

Units to sell to cover all costs.

Finance & InterestBasic

Profit

\text{Profit} = \text{Revenue} - \text{Cost}

The money left after subtracting cost from revenue.

Finance & InterestIntermediate

Break-Even Point

Q = \frac{FC}{P - VC}

Units to sell to cover all costs.

Finance & InterestBasic

Working Capital

WC = \text{Current Assets} - \text{Current Liabilities}

Short-term financial health of a business.

AccountingBasic

Accounting Equation

Assets = Liabilities + Equity

The foundation of double-entry bookkeeping: everything a business owns is financed either by debt or by owners’ capital.

AccountingBasic

Retained Earnings

RE_1 = RE_0 + NI - Dividends

Cumulative profit kept in the business rather than paid out to shareholders.

AccountingIntermediate

Retained Earnings

RE = RE_0 + NI - Dividends

Accumulated profit kept in the business.

Business & CommerceBasic

Selling Price from Markup

SP = Cost \times (1 + m)

The price to charge after adding a percentage markup to unit cost.

Business & CommerceBasic

Discounted Price

P = List \times (1 - d)

The final price after applying a percentage discount to the list price.

Business & CommerceBasic

Sales Tax

Total = Price \times (1 + t)

The amount payable once a sales-tax or VAT rate is added to the price.

Business & CommerceBasic

Revenue

Revenue = Price \times Quantity

Total income from sales before any costs are deducted.

Business & CommerceIntermediate

Contribution Margin

CM = Price - Variable\ Cost

The amount each unit sold contributes toward covering fixed costs and profit.

Business & CommerceIntermediate

Contribution Margin Ratio

CMR = \dfrac{Price - Variable\ Cost}{Price}

Contribution margin expressed as a fraction of the selling price.

Business & CommerceIntermediate

Break-Even (Units)

Q = \dfrac{Fixed\ Costs}{Price - Variable\ Cost}

The number of units that must be sold to exactly cover all costs.

Business & CommerceIntermediate

Margin of Safety

MoS = \dfrac{Sales - Break\text{-}even}{Sales}\times 100\%

How far sales can fall before the business hits its break-even point.

Business & CommerceIntermediate

Economic Order Quantity (EOQ)

EOQ = \sqrt{\dfrac{2DS}{H}}

The order size that minimizes total inventory ordering and holding costs.

Business & CommerceIntermediate

Customer Acquisition Cost (CAC)

CAC = \dfrac{Sales\ \&\ Marketing\ Cost}{New\ Customers}

The average cost to win one new customer.

Business & CommerceIntermediate

Customer Lifetime Value (CLV)

CLV = \dfrac{ARPU \times Gross\ Margin}{Churn\ Rate}

The total profit expected from a customer over the whole relationship.

Business & CommerceIntermediate

Churn Rate

Churn = \dfrac{Customers\ Lost}{Customers\ at\ Start}\times 100\%

The percentage of customers who stop buying over a period.

Business & CommerceIntermediate

Conversion Rate

CR = \dfrac{Conversions}{Visitors}\times 100\%

The share of visitors or leads that take the desired action.

Business & CommerceAdvanced

Month-over-Month Growth

g = \left(\dfrac{V_1}{V_0}\right) - 1

The percentage change in a metric from one period to the next.

Geography & EarthAdvanced

Haversine Distance

d = 2r\arcsin\sqrt{\sin^2\frac{\Delta\phi}{2} + \cos\phi_1\cos\phi_2\sin^2\frac{\Delta\lambda}{2}}

Great-circle distance between two lat/long points.