# Math Help - Cosine and Sine Help

1. ## 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.

2. Originally Posted by abstraktz
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".

3. thank you!