A-Level Maths: E6-12 Equivalent Forms: Solve 10sinθ - 6cosθ = 5

[TobstarXV]

If the question is stated as "Hence or otherwise find analytically all the solutions of 4sinTheta - 5cosTheta = 5" does that mean i have to go through all options/formulas like you did until i find the right one as well as showing my working out for the wrong formulas.

[ismailchoudhury]

Would it also work to use rsin(theta+alpha)

[taegan]

I tried to solve this using rcos(θ + α). My answers were correct for 2root34xcos(θ + 1.03) = 5 (i checked on a trig equation calculator), but they are not correct for the question. Instead of drawing the triangle I used tan(α) = sin(α)/cos(α) and sin^α + cos^α = 1. Do those trig identities only work if the angle is acute? My error seems to be in the process of falsely determining that 2root34xcos(θ + 1.03) is equal to the 10sinθ - 6cosθ...

[ryder]

Hi Jack, how did you get theta to be 3.24 when on the second intersection point where y=5, is shown on your sketch to be less than pi. 3.24 is obviously larger than pi but the second intersection point is between pi/2 and pi. Thanks

[everosie]

How do you do it if they give you the ending it in the form rcos(a+b) but you need to get it back to the original equation ??:)

[kuchbatein]

why cant we just take square on both sides?i did and it give me wrng answers...

[dannynoller]

Hi Jack,

Would squaring both sides and then using the identity sin^2(x)+cos^2(x)=1 in order to get an equation purely in sin or cos not work? If so, why not?

Thanks :)