The expression \( \cos x \) refers to the cosine of an angle \( x \). Cosine is one of the primary trigonometric functions and is defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle. Mathematically, for an angle \( x \), it's defined as:

\[
\cos x = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]

In terms of the unit circle, \( \cos x \) is the horizontal coordinate of the point on the unit circle corresponding to the angle \( x \) measured from the positive x-axis.

Do you want to evaluate \( \cos x \) for a specific value of \( x \) or delve into its properties?

Here are 5 questions to expand on this:

1. What is the value of \( \cos x \) when \( x = 0 \)?
2. How does \( \cos x \) behave as \( x \) approaches \( \pi/2 \)?
3. What is the derivative of \( \cos x \) with respect to \( x \)?
4. Can you express \( \cos x \) in terms of sine using an identity?
5. What is the Fourier series representation of a cosine function?

**Tip:** The cosine function is periodic with a period of \( 2\pi \), meaning \( \cos(x + 2\pi) = \cos x \).

Explore the cosine function in trigonometry, defined as the ratio of the adjacent side to the hypotenuse in a right triangle. Learn its key properties, including periodicity and its behavior on the unit circle. Suitable for students in Grades 10-12.

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