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