Auxilary angle help (1 Viewer)

[Pfortune35]

Im having some trouble with this auxilary angle stuff

the most common formla is rsin(Ɵ + A) = a sin Ɵ + b cos Ɵ

where r = sqrt (a^2 + b^2) and tan A = b/a

but there are 3 other formulas similar to this.

will i have to learn them all or will only one of them be enough?

 

[Drongoski]

If I'm not mistaken any one of the 4 will do. Why don't you just apply the one you learn to several questions and see. It is possible one formula gives you a cleaner solution than another. Try one out.

 

[michaeljennings]

the formula is rsin(theta + A)= rsinthetacosA + rsinAcostheta (that is just for sine though there is a formula for cosine) but basically they are the double angle formulas. When you expand out the double angle you compare coefficients on both sides to find two equations in terms of 'r' and then you use simultaneous equations to find r and then you sub 'r' back into your two equations and divide them by each other to find theta

 

[hscishard]

If you're don't like memorising, derive it then.

How you say? Read that guys post ^
Ignore the double angle bit. Think he meant trig expansions

 

[maths lover]

or u could equate coefficients, finding an expression of sin alpha and one for cos alpha and through division get what tan is equal to, hence finding alpha, and use the formula u have to find r. instead of:

the formula is rsin(theta + A)= rsinthetacosA + rsinAcostheta (that is just for sine though there is a formula for cosine) but basically they are the double angle formulas. When you expand out the double angle you compare coefficients on both sides to find two equations in terms of 'r' and then you use simultaneous equations to find r and then you sub 'r' back into your two equations and divide them by each other to find theta

and it helps to know two, one cos and one sine so that you can identify it quickly without messing around with the question to match up with the expansion.

 

[hscishard]

You basically said what he said...I think

 

[maths lover]

You basically said what he said...I think

no! he is for some reason using simultaneous equation.

 

[Alkanes]

Deriving the formula is the way to go for this topic.