ECE 4501 - TRIGNOMETRIC IDENTITIES – S.Norr

1. Sin A = Cos (A - 90°) ; Cos B = Sin (B + 90°)

2. Sin (A + B) = Sin A Cos B + Cos A Sin B

3. Sin (A – B) = Sin A Cos B – Cos A Sin B

4. Cos (A + B) = Cos A Cos B – Sin A Sin B

5. Cos (A – B) = Cos A Cos B + Sin A Sin B

6. Cos A Cos B = ½ [ Cos (A – B) + Cos (A + B) ]

7. Sin A Sin B = ½ [ Cos (A – B) – Cos (A + B) ]

8. Sin A Cos B = ½ [ Sin (A + B) + Sin (A – B) ]

9. Cos A Sin B = ½ [ Sin (A + B) – Sin (A – B) ]

10. Sin² A = ½ (1 – Cos 2A)

11. Cos²A = ½ (1 + Cos 2A)

12. Sin A Cos A = ½ Sin 2A

13. A Cos wt + B Sin wt = C Cos (wt - a) Where: C = (A² + B²) ^½

a = Tan^-1 B/A

14. Sec² A = 1 + Tan² A

15. Law of Sines: a = b = c__ Sin A Sin B Sin C
16. Law of Cosines: a^2 = b^2 +c^2 – 2 b c Cos A

17. Euler’s Identities: e^{± jq} = Cos q ± j Sin q

Cos q = e^jq + e^{- jq}

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Sin q = e^jq - e^{- jq}

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