Multiple Angle Identities for Cosine

Multiple Angle Identities for Cosine

Each of these identities expresses the cosine function of an angle that is a multiple of another angle in terms of the cosine function of the original angle.  

2.  (Double angle identity for cosine)

3. (Triple angle identity for cosine)

4. (Quadruple angle identity for cosine)

5. (Quintuple angle identity for cosine)

6. (Sextuple angle identity for cosine)

7. (Septic angle identity for cosine)

8.

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20.

Multiple Angle Identities for Hyperbolic Cosine

Multiple Angle Identities for Hyperbolic Cosine

2. (Double angle identity for hyperbolic cosine)

3. (Triple angle identity for hyperbolic cosine)

4. (Quadruple angle identity for hyperbolic cosine)

5. (Quintuple angle identity for hyperbolic cosine)

6.

7.

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Multiple Angle Identities for Hyperbolic Tangent

Multiple Angle Identities for Hyperbolic Tangent

2. (Double angle identity for hyperbolic tangent)

3. (Triple angle identity for hyperbolic tangent)

4. (Quadruple angle identity for hyperbolic tangent)

5. (Quintuple angle identity for hyperbolic tangent)

6. (Sextuple angle identity for hyperbolic tangent)

7.

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10.

11.

12. 

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18.

19.

In-Text or Website Citation

Tue N. Vu, Multiple Angle Identities for Hyperbolic Tangent from Series Math Study Resource.

Hyperlink: http://www.seriesmathstudy.com/sms/multiple_angle_hyper_tangent

Multiple Angle Identities for Tangent

Multiple Angle Identities for Tangent

2. (Double angle identity for tangent)

3. (Triple angle identity for tangent)

4. (Quadruple angle identity for tangent)

5.  (Quintuple angle identity for tangent)

6. (Sextuple angle identity for tangent)

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

Tue N. Vu, Multiple Angle Identities for Tangent from Series Math Study Resource.

Hyperlink: http://www.seriesmathstudy.com/sms/multiple_angle_tangent