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    Express 4sinx + 3cosx in the form Rsin(x+ angle) , where R>0 and 0<angle<pi/2 = 5sin(x + 0.644).
    State the minimum value of 4sinx and 3cosx and the smallest positive value of x for which this minimum value occurs.

    How do i find the minimum value and the smallest positive value of x??
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    Apply the R formula and think about how it's a transformation of the sin function and therefore deduce the answers.
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    (Original post by Chelsea12345)
    Express 4sinx + 3cosx in the form Rsin(x+ angle) , where R>0 and 0<angle<pi/2 = 5sin(x + 0.644).
    State the minimum value of 4sinx and 3cosx and the smallest positive value of x for which this minimum value occurs.

    How do i find the minimum value and the smallest positive value of x??
    The way you worded it makes it seem as if the question is directed at 4sinx and 3cosx separately, rather than 4sinx+3cosx

    Anyway, the minimum of 4\sin x + 3 \cos x is the same as the minimum of 5\sin (x+0.644). What is the minimum of the sine function? Hence what's the minimum of 5\sin(x+0.644)?

    For the smallest positive value of x, you take the min value you find above, and make it equal to 5\sin(x+0.644) and solve the equation for x. Choose x to be the smallest +ve solution, obviously.
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    thankyou
 
 
 
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