Negative angle identities describe how trigonometric functions behave when the input angle is negated. These are also called even-odd identities because they classify trig functions as even (cosine, secant) or odd (sine, tangent, cosecant, cotangent).
⚠Even functions are symmetric about the y-axis (cos(-A)=cosA). Odd functions are symmetric about the origin (sin(-A)=-sinA).
What Are Negative Angle Identities?
Negative angle identities determine the value of trigonometric functions at the negative of an angle. They are derived from the geometric symmetry of the unit circle where a negative angle represents clockwise rotation.
Odd Functions
sin, tan, csc, cot are odd: f(-x) = -f(x). The function value changes sign when the input is negated.
Even Functions
cos and sec are even: f(-x) = f(x). The function value stays the same when the input is negated.
Unit Circle Symmetry
Point at -A is the reflection of point at A across the x-axis. x-coordinate (cos) stays same, y-coordinate (sin) flips.
Function Classification
Remember: Even functions = cosine and secant (positive). Odd functions = sine, tangent, cosecant, cotangent (sign changes).
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.