Fundamental Trigonometric Identities

A step-by-step guide to fundamental trigonometric identities

The basic trigonometric identities or fundamental trigonometric identities are those trigonometric functions that are true every time for the variables.

The following equations are eight of the most basic and important trigonometric identities. These equations are true for any angle. Countless additional identities can be formed from them. These eight things should be kept in mind.

• \(\color{blue}{cot\left(θ\right)=\frac{cos\:\left(\theta \right)}{sin\:\left(\theta \right)}}\)
• \(\color{blue}{tan⁡\:\left(\theta \right)=\frac{sin\:\left(\theta \right)}{cos\:\left(\theta \right)}}\)
• \(\color{blue}{cot\left(θ\right)=\frac{1}{tan\:\left(\theta \right)}}\)
• \(\color{blue}{sec\left(θ\right)=\frac{1}{cos\:\left(\theta \right)}}\)
• \(\color{blue}{csc\left(θ\right)=\frac{1}{sin\:\left(\theta \right)}}\)
• \(\color{blue}{\left(sin\left(θ\right)\right)^2+\left(cos\left(θ\right)\right)^2=1}\)
• \(\color{blue}{1+\left(tan\left(θ\right)\right)^2=\left(sec\left(θ\right)\right)^2\:\:}\)
• \(\color{blue}{1+\left(cot\left(θ\right)\right)^2=\left(csc\left(θ\right)\right)^2}\)