Today's soundtrack is *Behemoth: Demigod*, a death metal album with dark lyrics based on themes found in ancient folklore and religions.

This afternoon, I'm working on the last lesson in this unit; this unit is the last unit in this module; so I'll be writing my third of the four module tests this week.

This unit deals with Double Angle Identities. These tell us what happens if both *a* and *b* are equal to θ.

There are three categories of double angle identities: sin, cos, and tan.

**Double Angle Identities**

**Sine**Sin2θ =

**2sinθcosθ****Cosine**Cos2θ =

**cos²θ - sin²θ**Cos2θ =

**2cos²θ - 1**Cos2θ =

**1- 2sin²θ****Tangent**Tan2θ =

**(2tanθ) / (1-tan²θ)**

If we see the constants changed (for example from 1-2sin²θ to 3-6sin²θ), obviously it will no longer equal cos2θ; we take the factor that the identity has been changed by and we precede our function with that value. So 3-6sin²θ = 3cos2θ.

To determine the restrictions of a trigonometric expression, we must ensure that the denominator ≠ 0. To do so, we must find all forms of the denominator if it is a trigonometric identity and list any that, if they were to equal zero, would make the whole denominator zero.

That's it for today! Next time, I'm going to be
*s t u d y i n g*