Hi I really don't know to do this problem.

The equation cos(3x) = 1/2

has two solutions between 0 and 120 degrees. The smaller is _____ degrees and the larger is _______ degrees.

Am I suppose to take cos(pi/3) / 3 and thats my answer?

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- Dec 4th 2005, 08:47 PMkillasnakeTrig problem (cos)
Hi I really don't know to do this problem.

The equation cos(3x) = 1/2

has two solutions between 0 and 120 degrees. The smaller is _____ degrees and the larger is _______ degrees.

Am I suppose to take cos(pi/3) / 3 and thats my answer? - Dec 5th 2005, 03:40 AMticbolQuote:

Originally Posted by**killasnake**

Instead, you are supposed to get the the arccosine of (1/2), and equate those to 3x to find x.

cos(3x) = 1/2

That means the cosine of an angle, here it is 3x, is positive 1/2.

In the 4 quadrants, where is cosine value positive?

Cosine is positive where the x-coordinate is positive. The x-coordinate is positive to the right of the y-axis, or at the 1st and 4th quadrants. Hence, the angle 3x is in the 1st or 4th quadrant.

cos(3x) = 1/2

3x = arccos(1/2)

3x = 60 degrees in the 1st quadrant.

3x = 360 -60 = 300 degrees in the 4th quadrant.

Therefore, x = 60/3 = 20 degrees.

or, x = 300/3 = 100 degrees. - Dec 5th 2005, 03:02 PMkillasnake
oh! Thank you for the explanation.