Math Problem Statement

Complete the table for each value of x in radians: cos(0), cos(π/2), cos(π), cos(3π/2), cos(2π).

Solution

The image asks to complete the table for values of cos(x)\cos(x) for specific values of xx in radians. Let's go through the values of xx given and compute cos(x)\cos(x).

  1. x=0x = 0: cos(0)=1\cos(0) = 1 This value is already provided.

  2. x=π2x = \frac{\pi}{2}: cos(π2)=0\cos\left(\frac{\pi}{2}\right) = 0 The empty box should be filled with 0.

  3. x=πx = \pi: cos(π)=1\cos(\pi) = -1 This value is already provided.

  4. x=3π2x = \frac{3\pi}{2}: cos(3π2)=0\cos\left(\frac{3\pi}{2}\right) = 0 The empty box should be filled with 0.

  5. x=2πx = 2\pi: cos(2π)=1\cos(2\pi) = 1 The empty box should be filled with 1.

Completed Table:

  • cos(0)=1\cos(0) = 1
  • cos(π2)=0\cos\left(\frac{\pi}{2}\right) = 0
  • cos(π)=1\cos(\pi) = -1
  • cos(3π2)=0\cos\left(\frac{3\pi}{2}\right) = 0
  • cos(2π)=1\cos(2\pi) = 1

Let me know if you'd like more details or have further questions.

Relative Questions:

  1. What is the general formula for the cosine function for any angle?
  2. Can you

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Unit Circle
Cosine Function

Formulas

cos(θ)

Theorems

Cosine values on the unit circle

Suitable Grade Level

Grades 9-12