# Maths

a) Express f(theta) = 4cos theta - 6sin theta in the form r cos(theta + alpha)

b) Hence find the general solution of the equation 4cos theta - 6sin theta =5

c) Hence, find the minimum value of the function 1/4+f( theta)

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1. √(4^2+6^2) = √52
so you need
sin alpha = 4/√52 = 2/√13
cos alpha = 6/√52 = 3/√13
see what you can do with that ...

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posted by Becky
3. c'mon, the whole point of part a was to prepare you to write
f(θ) = √52 (4/√52 cosθ - 6/√52 sinθ)
= √52 (sinα cosθ - cosα sinθ)
= √52 sin(α-θ)

You now know what the max/min values of f(θ) are, so you can easily answer part c.

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