Math Problem Statement

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

Solution

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

To solve this:

  1. The cosine of 330330^\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)\cos(330^\circ) is simply 330330^\circ, but we are asked for its principal value, which should lie between 00^\circ and 360360^\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 330330^\circ, it is its own principal argument.

Now, looking at the options in the image:

  1. 00^\circ
  2. 180180^\circ
  3. 270270^\circ
  4. 300300^\circ

The correct answer is 300°, as cos(330)\cos(330^\circ) is equivalent to cos(300)\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.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Angles in Standard Position
Unit Circle

Formulas

cos(θ) for standard angles on the unit circle

Theorems

Unit Circle Theorem
Principal Value of Trigonometric Functions

Suitable Grade Level

Grades 10-12