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Math Help - Cosine and Sine Help

  1. #1
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    Cosine and Sine Help

    Hello, there are two problems that I am stuck on. Any help will be appreciated thank you.

    1. Explain why e^cos x < 3 for every real number x.

    2. Explain why there does not exist a number theta such that: log cos(theta) = 0.1.
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  2. #2
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    Quote Originally Posted by abstraktz View Post
    Hello, there are two problems that I am stuck on. Any help will be appreciated thank you.

    1. Explain why e^cos x < 3 for every real number x.

    2. Explain why there does not exist a number theta such that: log cos(theta) = 0.1.
    1. The exponent (that is cos x) is never larger than 1 ....

    2. Assuming base 10, you have 10^{0.1} = \cos \theta and it should be clear that 10^{0.1} > 1 .... By the way, a number theta does exist (in fact, an infinite number of values exist) but it's not real. The question should be worded as "Explain why there does not exist a real number theta such that: log cos(theta) = 0.1".
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  3. #3
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    thank you!
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