# SAT Math Multiple Choice Question 627: Answer and Explanation

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**Question: 627**

**12.** 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:** B

**Explanation:**

**B**

**Special Topics (trigonometry) MEDIUM-HARD**

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:

What does the mean in terms of the unit circle? Recall from Chapter 10, Lesson 9, that 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.