• Algebra
• Trigonometry
• Geometry
• Calculus

Negative angle identities

There are six negative angle trigonometric identities in trigonometry and they are used as formulas when trigonometric functions appear with negative angles. The negative angle identities are helpful to transform any trigonometric function which contains negative angle as same trigonometric ratio with positive angle.

$(1) \,\,\,\,\,\,$ $\sin{(-\theta)} \,=\, -\sin{\theta}$

Sine of negative angle is equal to negative sine of angle.

$(2) \,\,\,\,\,\,$ $\cos{(-\theta)} \,=\, \cos{\theta}$

Cosine of negative angle is equal to cosine of angle.

$(3) \,\,\,\,\,\,$ $\tan{(-\theta)} \,=\, -\tan{\theta}$

Tangent of negative angle is equal to negative tangent of angle.

$(4) \,\,\,\,\,\,$ $\cot{(-\theta)} \,=\, -\cot{\theta}$

Cotangent of negative angle is equal to negative cotangent of angle.

$(5) \,\,\,\,\,\,$ $\sec{(-\theta)} \,=\, \sec{\theta}$

Secant of negative angle is equal to secant of angle.

$(6) \,\,\,\,\,\,$ $\csc{(-\theta)} \,=\, -\csc{\theta}$

Cotangent of negative angle is equal to negative cotangent of angle.