Trigonometric Identities

32 flashcards · Mathematics · by John Wilson III

1. sin2θ + cos2θ =

   1

2. tan2θ + 1 =

   sec2θ

3. 1 + cot2θ =

   csc2θ

4. sin2θ =

   1 - cos2θ

5. tan2θ =

   sec2θ - 1

6. cot2θ =

   csc2θ - 1

7. tan2θ - sec2θ =

   1

8. csc2θ - cot2θ =

   1

9. cscθ =

   1 sin(θ)

10. secθ =

    1 cos (θ)

11. cotθ =

    1 tan(θ)

12. tan( a+ba+ba+b ) =

    tan( aaa ) + tan( bbb ) 1 - tan( aaa ) tan( bbb )

13. tan( a−ba-ba−b ) =

    tan( aaa ) - tan( bbb ) 1 + tan( aaa ) tan( bbb )

14. cos(π/2 - θ) =

    sin θ

15. sin(π/2 - θ) =

    cos θ

16. sin (a+b)(a + b)(a+b) =

    sin( aaa ) cos( bbb ) + cos( aaa ) sin( bbb )

17. sin (a−b)(a - b)(a−b) =

    sin( aaa ) cos( bbb ) - cos( aaa ) sin( bbb )

18. cos (a+b)(a + b)(a+b) =

    cos( aaa ) cos( bbb ) - sin( aaa ) sin( bbb )

19. cos (a−b)(a - b)(a−b) =

    cos( aaa ) cos( bbb ) + sin( aaa ) sin( bbb )

20. sin(2θ) =

    2 sinθ cosθ

21. cos(2θ) =

    cos2θ - sin2θ and 1 - 2 sin2θ and 2 cos2θ - 1

22. tan(2θ) =

    2 tanθ 1 - tan2 θ

23. sin2θ =

    1 - cos(2θ) 2

24. cos2θ =

    1 + cos(2θ) 2

25. tan2θ =

    1 - cos(2θ) 1 + cos(2θ)

26. sin2(θ/2) =

    1 - cosθ 2

27. cos2(θ/2) =

    1 + cosθ 2

28. tan2(θ/2) =

    1 - cosθ 1 + cosθ

29. sin(θ/2) =

30. cos(θ/2) =

31. tan(θ/2) =