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Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.

To find the value of R, use Pythagoras's Theorem using the coeffecients of cos θ and sin θ. The correct answer should be R=5. Expand the expression  R cos(θ – α). Equate the expanded expression with 3 cos θ + 4 sin θ to find the value of θ. The correct answer is α = 53...° approximately.

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