Teoria Relações trigonométricas

Abaixo apresentamos um resumo das identidades trigonométricas:

Somando $\frac{\pi}{2}$:
$$\bullet\;\; \sin\left(\alpha + \frac{\pi}{2}\right) = \cos\alpha$$

$$\bullet\;\;\cos\left(\alpha + \frac{\pi}{2}\right) =- \sin\alpha$$

$$\bullet\;\;\tan\left(\alpha + \frac{\pi}{2}\right) =- \cot\alpha$$

$$\bullet\;\;\csc\left(\alpha + \frac{\pi}{2}\right) = \sec\alpha$$

$$\bullet\;\;\sec\left(\alpha + \frac{\pi}{2}\right) =- \csc\alpha$$

Somando $\pi$:
$$\bullet\;\; \sin\left(\alpha + \pi\right) = -\sin\alpha$$

$$\bullet\;\;\cos\left(\alpha + \pi\right) = -\cos\alpha$$

$$\bullet\;\;\tan\left(\alpha + \pi\right) = \tan\alpha$$

$$\bullet\;\;\cot\left(\alpha + \pi\right) = \cot\alpha$$

$$\bullet\;\;\csc\left(\alpha + \pi\right) = -\csc\alpha$$

$$\bullet\;\;\sec\left(\alpha + \pi\right) = -\sec\alpha$$