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C4 MEI Harmonic Form

Doing some questions on harmonic form and I am getting stuck in some places that I thought I understood in class.

What dictates which order your A and B are when you do arctan(B/A) ?
What dictates whether or not it's a + or a - in the translation of the X?

Question:

Spoiler

(edited 8 years ago)
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Original post by drakansteal
Doing some questions on harmonic form and I am getting stuck in some places that I thought I understood in class.

What dictates which order your A and B are when you do arctan(B/A) ?
What dictates whether or not it's a + or a - in the translation of the X?

Question:

Spoiler



Rcos(θ±α)=RcosαcosθRsinαsinθR\cos(\theta \pm \alpha) = R\cos \alpha \cos \theta \mp R\sin \alpha\sin \theta, so, for example, in (i):

Rcosα=1R \cos \alpha = 1 and Rsinα=1R \sin \alpha = 1 and you take the (+) so you're using Rcos(xα)R \cos (x -\alpha), hence:

Squaring the first two equations and adding: R2(cos2α+sin2α)=1    R2=1R^2 (\cos^2 \alpha + \sin^2 \alpha) = 1 \iff R^2 = 1

Dividing the second equation by the first: RsinαRcosα=11    tanα=1\displaystyle \frac{R \sin \alpha}{R \cos \alpha} = \frac{1}{1} \iff \tan \alpha = 1

What equations would you get for (ii)?
(edited 8 years ago)

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