How to Graph Cosine Degrees

Imagine moving along a circular path totaling 360 steps and recording the coordinates of your position at every step. By graphing the cosine function, you create a visual map of how the x-axis projection of every position on the circumference changes as you travel counterclockwise around the circle. The cosine graph resembles a wave, starting high, dipping low and ending at a high point. As you draw the cosine graph, you track the decrease and increase in the length of the projection of each circumference point onto the horizontal axis.

Things You'll Need

  • Pencil
  • Ruler
  • Paper
  • Graph paper
  • Calculator
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Instructions

    • 1

      Draw and label the x- and y-axes of the graph. The horizontal x-axis is labeled as x, where x is measured in degrees. The vertical y-axis is labeled as y, where y is a function of x. The function y can be written as y = cosine (x).

    • 2

      Mark and label the intervals on the x- and y-axes. The x-axis covers the range of 0 to 360 degrees. The y-axis covers the range -1 to +1. For example, the x-axis can be divided into 10 degree intervals, while the y-axis is divided into intervals of 0.1.

    • 3

      Make a table with 2 columns. The first column represents the x-values; the second column represents the y-values of each point on the graph. Fill the first column with integers from the range of 0 to 360 degrees. You don't need to include all the integers in this range. Choose integers at regular intervals. However, the more integers you include, the more accurate your graph will be. For example, you could include the integers 0, 10, 20, 30, 40... 360 in your table. Use the cosine function on your calculator to calculate the corresponding values for the second column: y = cosine (x). For example, the second column would include +1, +0.98, +0.94, + 0.86, +0.76... +1 = y = cosine (x) = cosine (0), cosine (10), cosine (20), cosine (30), cosine (40)... cosine (360).

    • 4

      Plot all the (x, y) points from your table on the graph. Place a pencil dot on the graph paper to represent each point.

    • 5

      Draw a line through the points. The line should follow a wave curve that starts at the highest point on the graph (0; +1), dips to the lowest point (180, -1), and ends at the highest point (360; +1).

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