One way of solving this function is by graphing the trig function as written here (making sure that your calculator or graphing utility is set to "radians" instead of "degrees"). To do this, you can simply enter y = cos(3x) and then graph a second line at y = (2/3). The latter will be a straight line. You can then locate at which x-values they intercept. These include decimals +/- .28, and +/- 1.184 (in radians).

As a slight adjustment to this, you can alternatively graph y = cos(3x) - 2/3 and look for the x-intercepts (the values will be the same).

Or, as stated by another Educator, you can use the inverse cosine function to write x = (1/3)arccos(2/3).

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