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How many solutions to the equation 4 cos x = 1 lie between x = 0 and x = 3π
- a)Two
- b)Three
- c)Four
- d)Six
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
How many solutions to the equation 4 cos x = 1 lie between x = 0 and x...
In order to solve this without a calculator, we need to know how to analyze this problem in terms of the unit circle. First, let’s solve for cos x: 4 cos x = 1
Divide by 4: cos x = 1/4
the cosine of any angle corresponds to the x-coordinate of the corresponding point for that angle on the unit circle:
Divide by 4: cos x = 1/4
the cosine of any angle corresponds to the x-coordinate of the corresponding point for that angle on the unit circle:
Notice that there are exactly two points on the unit circle that have an x-coordinate of 1/4. Now let’s think about the angle. We are told that x goes from 0 to 3π. Remember that a full trip around the circle is 2π radians; therefore, a journey from x = 0 to x = 3π is 1.5 trips around the circle counterclockwise starting from the positive x-axis. If you trace with your finger 1.5 times around the circle starting from the point (1, 0), you’ll hit our “points of interest” exactly three times.
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How many solutions to the equation 4 cos x = 1 lie between x = 0 and x = 3πa)Twob)Threec)Fourd)SixCorrect answer is option 'B'. Can you explain this answer?
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