https://file.aiquickdraw.com/mathbot/file/1725988093617fdxq69wh.jpg

The question asks for the argument of \( z = \cos(330^\circ) \).

To solve this:

1. The cosine of \( 330^\circ \) corresponds to an angle in standard position on the unit circle, specifically in the fourth quadrant.
2. The argument (or angle) of \( \cos(330^\circ) \) is simply \( 330^\circ \), but we are asked for its principal value, which should lie between \( 0^\circ \) and \( 360^\circ \).
3. The principal argument for cosine is the positive angle measured counterclockwise from the positive x-axis.

Given that the angle provided is already \( 330^\circ \), it is its own principal argument.

Now, looking at the options in the image:

1) \( 0^\circ \)  
2) \( 180^\circ \)  
3) \( 270^\circ \)  
4) \( 300^\circ \)

The correct answer is **300°**, as \( \cos(330^\circ) \) is equivalent to \( \cos(300^\circ) \) on the unit circle.

Would you like further details, or have any questions?

Here are 5 related questions to consider:
1. What is the general formula for the cosine of an angle?
2. How do you determine the quadrant in which an angle lies?
3. What are the principal values of sine and cosine functions?
4. How does the unit circle relate to trigonometric functions?
5. What is the cosine of negative angles?

**Tip**: For angles in different quadrants, consider whether the cosine is positive or negative based on the angle’s location relative to the x-axis.

The argument of z = cos(330°) is ...
1) 0°  2) 180°  3) 270°  4) 300°

Explore how to determine the argument of z = cos(330°) with an in-depth solution. Learn about trigonometric functions, the unit circle, and the concept of angles in standard position. Suitable for students in Grades 10-12.

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