To calculate \( \cos(-1.1\pi) \), let's proceed as follows:

1. First, recognize that \( \cos(-\theta) = \cos(\theta) \), so we can rewrite \( \cos(-1.1\pi) \) as \( \cos(1.1\pi) \).
   
2. \( 1.1\pi \) is equivalent to \( \pi + 0.1\pi \), which is approximately \( \pi + 0.314 \).

3. Since \( \pi \) is at 180° and adding 0.1π (or about 18°), we are in the third quadrant where cosine values are negative.

4. Now calculate \( \cos(1.1\pi) \):
   \[
   \cos(1.1\pi) \approx -\cos(0.1\pi)
   \]
   Using a calculator or knowing \( \cos(0.1\pi) \approx 0.9511 \), we get:
   \[
   \cos(1.1\pi) \approx -0.9511
   \]

So, \( \cos(-1.1\pi) \approx -0.9511 \).

Would you like more details on any step, or do you have any questions?

1. What is the effect of the negative angle on trigonometric functions?
2. How can we use trigonometric identities to simplify angle calculations?
3. What is the value of \( \sin(-1.1\pi) \)?
4. How does cosine behave in different quadrants?
5. Can we convert \( -1.1\pi \) to degrees and solve?

**Tip:** Remember, \( \cos(-\theta) = \cos(\theta) \) because cosine is an even function.

Learn how to calculate cos(-1.1π) by applying trigonometric identities and understanding cosine behavior in different quadrants. This guide covers the properties of even functions, angle transformations, and more. Suitable for students in Grades 9-11.

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