JUNE 2006 (i) Express 7 cos ? + 24 sin ? in the form R cos(? ? ?), where R > 0 and 0 < ? < 90, giving the exact value of R and the value of ? correct to 2 decimal places. (ii) Hence solve the equation 7 cos ? + 24 sin ? = 15, giving all solutions in the interval 0 ? ? ? 360.
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To do this, we use the identity \(a \cos \theta + b \sin \theta = R \cos (\theta - \alpha)\), where \(R = \sqrt{a^2 + b^2}\) and \(\tan \alpha = \frac{b}{a}\). Show more…
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