Fundamental Trigonometric Identities

Flashcards representing key concepts and identities pertaining to fundamental trigonometric identities, their relationships, and applications related to triangles.

Reciprocal Identities

Relationships involving the reciprocal functions: csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.

Quotient Identities

Identities that define tangent and cotangent in terms of sine and cosine: tan θ = sin θ/cos θ, cot θ = cos θ/sin θ.

Pythagorean Identities

Identities derived from the Pythagorean theorem: sin²θ + cos²θ = 1, 1 + cot²θ = csc²θ, tan²θ + 1 = sec²θ.

Cofunction Identities

Relationships between trigonometric functions of complementary angles: sin(π/2 - θ) = cos θ, and others.

Even – Odd Identities

Properties of trigonometric functions that govern their symmetry: sin(-θ) = -sin θ, cos(-θ) = cos θ.

Sum and Difference Identities

Formulas for the sine and cosine of sums or differences of angles.

Double-Angle Identities

Formulas that express trigonometric functions of double angles in terms of single angles.

Half-Angle Identities

Formulas that express functions of half angles in terms of single angles.

Power-Reducing Formulas

Formulas that reduce powers of sine and cosine functions.

Product-to-Sum Formulas

Formulas that express products of sine and cosine functions as sums.

Sum-to-Product Formulas

Formulas that express sums of sine and cosine functions as products.

Law of Sines

A formula relating the ratios of the sides of a triangle to the sine of its angles.

Law of Cosines

A formula used to calculate a side of a triangle when two sides and the included angle are known.

Area of an Oblique Triangle

The formula for finding the area of a triangle given two sides and an angle between them: Area = (1/2)bc sin A.