Trigonometric Identities

A set of flashcards focusing on trigonometric identities, covering reciprocal, quotient, Pythagorean, cofunction, and even/odd identities.

Reciprocal Identities

Identities that relate sine, cosine, and tangent to their corresponding cosecant, secant, and cotangent.

sin x

The sine function describes the ratio of the opposite side to the hypotenuse in a right triangle.

Quotient Identities

Identities that express tangent and cotangent in terms of sine and cosine.

tan x

The tangent function, defined as the ratio of sine to cosine.

cot x

The cotangent function, defined as the ratio of cosine to sine.

Pythagorean Identities

Trigonometric identities derived from the Pythagorean theorem involving sine, cosine, tangent, secant, and cosecant.

sin²x + cos²x = 1

The fundamental Pythagorean identity.

1 + tan²x = sec²x

Related identity that connects tangent and secant.

cot²x + 1 = csc²x

Identity relating cotangent and cosecant.

Cofunction Identities

Identities that express the relationships between trigonometric functions of complementary angles.

sin(π/2 - x) = cos x

Cofunction identity between sine and cosine.

tan(π/2 - x) = cot x

Cofunction identity between tangent and cotangent.

Even/Odd Identities

Identities that describe the symmetry of trigonometric functions.

sin(-x) = -sin x

Identity showing sine is an odd function.

cos(-x) = cos x

Identity showing cosine is an even function.

tan(-x) = -tan x

Identity showing tangent is an odd function.

csc(-x) = -csc x

Identity showing cosecant is an odd function.

sec(-x) = sec x

Identity showing secant is an even function.

Adding zero

An operation that does not change the value of a function.

Multiplying by 1

An operation that does not change the value of a function.

Collinearity

A condition where points lie on the same straight line in a geometric sense.

Identity

An equation that is true for all values of the variable.

Function

A relation that uniquely associates an input with exactly one output.

Trigonometric Function

Functions that relate angles to the ratios of the sides of triangles.

Angle

The figure formed by two rays, called the sides of the angle, sharing a common endpoint.

Ratio

A relationship between two numbers indicating how many times the first number contains the second.