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Question

Write the interval in which the value of 5 cos x + 3 cos x+π3+3 lies.

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Solution

Let fx=5 cosx+3 cosx+π3+3 =5 cosx+3(cosx cos60° -sinx sin60°) +3 =5 cosx+32cosx-332sinx +3 =132cosx-332sinx +3We know that-1322+3322132cosx-332sinx1322+3322-1694+274132cosx-332sinx1694+274-142132cosx-332sinx142-7+3132cosx-332sinx+37+3Hence, f(x) lies in the interval -4,10.

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