Tablas y Fórmulas

Tablas y Fórmulas

Identidades Trigonometricas

Identidades básicas
1. $\sin\theta=\dfrac{1}{\csc\theta}$

2. $\cos\theta=\dfrac{1}{\sec\theta}$

3. $\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{1}{\cot\theta}$

4. $\csc\theta=\dfrac{1}{\sin\theta}$

5. $\sec\theta=\dfrac{1}{\cos\theta}$

6. $\cot\theta=\dfrac{\cos\theta}{\sin\theta}=\dfrac{1}{\tan\theta}$

Identidades Pitagoricas

7. $\sin^{2}\theta+\cos^{2}\theta=1$

8. $1+\tan^{2}\theta=\sec^{2}\theta$

9. $1+\cot^{2}\theta=\csc^{2}\theta$

Identidades de Suma/Resta

10. $\sin(\theta+\beta)=\sin\theta \cos\beta+\sin\beta \cos\theta$

11. $\sin(\theta-\beta)=\sin\theta \cos\beta-\sin\beta \cos\theta$

12. $\cos(\theta+\beta)=\cos\theta \cos\beta-\sin\theta \sin\beta$

13. $\cos(\theta-\beta)=\cos\theta \cos\beta+\sin\theta \sin\beta$

14. $\tan\left(\theta+\beta\right)=\dfrac{\tan\theta+\tan\beta}{1-\tan\theta \tan\beta}$

15. $\tan\left(\theta-\beta\right)=\dfrac{\tan\theta-\tan\beta}{1+\tan\theta \tan\beta}$

Identidades de Ángulo Medio

16. $\sin^{2}\left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos\theta}{2}$

17. $\cos^{2}\left(\dfrac{\theta}{2}\right)=\dfrac{1+\cos\theta}{2}$

18. $\tan^{2}\left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos\theta}{1+\cos\theta}$

Identidades de Ángulo Doble

19. $\sin\left(2\theta\right)=2\sin\theta \cos\theta$

20. $\cos(2\theta)=\cos^{2}\theta-\sin^{2}\theta$

21. $\cos\left(2\theta\right)=1-2\sin^{2}\theta$

22. $\cos\left(2\theta\right)=2\cos^{2}\theta-1$

23. $\tan\left(2\theta\right)=\dfrac{2\tan\theta}{1-\tan^{2}\theta}$

Identidades de Suma a Producto

24. $\sin\theta+\sin\beta=2\sin\left(\dfrac{\theta+\beta}{2}\right)\cos\left(\dfrac{\theta-\beta}{2}\right)$

25. $\sin\theta-\sin\beta=2\sin\left(\dfrac{\theta-\beta}{2}\right)\cos\left(\dfrac{\theta+\beta}{2}\right)$

26. $\cos\theta+\cos\beta=2\cos\left(\dfrac{\theta+\beta}{2}\right)\cos\left(\dfrac{\theta-\beta}{2}\right)$

27. $\cos\theta-\cos\beta=-2\sin\left(\dfrac{\theta+\beta}{2}\right)\sin\left(\dfrac{\theta-\beta}{2}\right)$

Identidades de Producto a Suma

28. $\sin\beta\cos\theta=\frac{1}{2}\left[\sin\left(\beta+\theta\right)+\sin\left(\beta-\theta\right)\right]$

29. $\cos\beta\sin\theta=\frac{1}{2}\left[\sin\left(\beta+\theta\right)-\sin\left(\beta-\theta\right)\right]$

30. $\cos\beta\cos\theta=\frac{1}{2}\left[\cos\left(\beta+\theta\right)+\cos\left(\beta-\theta\right)\right]$

31. $\sin\beta\sin\theta=\frac{1}{2}\left[\cos\left(\beta-\theta\right)-\cos\left(\beta+\theta\right)\right]$

Identidades Función Par Impar