SAT Math Multiple Choice Question 748: Answer and Explanation
13. For how many values of x between 0 and 2π does sin
- A. Two
- B. Three
- C. Four
- D. Six
Correct Answer: D
Special Topics (trigonometry) HARD
Although this question can be solved by graphing, it is simpler and more efficient to imagine the unit circle, as we discussed in Chapter 10, Lesson 9.
We are asked to consider those angles that have a sine of ½. As you recall from Chapter 10, Lesson 9, the angles whose sine is ½ correspond to those angles that intersect the unit circle at any point where y = ½, as shown in the diagram above. Notice that the line y = ½ intersects the unit circle in two points. We are asked to consider sin 3x, where x takes values from 0 to 2π. This means that 3x takes values from 0 to 6π. In other words, we are taking three complete trips around the unit circle (since each trip around is 2π radians). How many times will we visit those two points if we take three trips around the circle? Clearly (3)(2) = 6 times.