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**madmax29** Compound Angle problems

I have the equation 5.5 Cos t + 7.8 Sin t

i) i have to express it in the form R Sin (t + ᾀ) <---- ᾀ alpha)

ii) solve for 0 < Θ < 2Π for 5.5 Cos t + 7.8 Sin t = 4.5

for part i) got 5.5 Cos t + 7.8 Sin t = R Sin (t + ᾀ)

where = R[sin t Cos ᾀ + Cos t Sin ᾀ]

= (R Cos ᾀ) Sin t + (R Sin ᾀ) Cos t

the next stage i have to get it into R = SQUAREROOT(a^2 + b^2)

unsure how to do this???

also my current attemp at part ii has led me with incorrect answers?? any help?