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Find values of x on the interval [0,pi] ...

Find values of x on the interval `[0,pi]` for which `cos x le sin 2x`.

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To solve the inequality \( \cos x \leq \sin 2x \) on the interval \( [0, \pi] \), we will follow these steps: ### Step 1: Rewrite the inequality We start with the inequality: \[ \cos x \leq \sin 2x \] Using the double angle formula for sine, we know that: ...
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Knowledge Check

  • Find the intervals in which f(x)=log(cosx), 0 le x le 2pi is increasing.

    A
    `(pi/2, pi) cup ((3pi)/2, 2pi)`
    B
    `(0, pi/2) cup ((3pi)/2)`
    C
    `[0, pi]`
    D
    `(pi/2, (3pi)/2)`

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