The number of values of in the interval satisfying the equation is
- A.0
- B.5
- C.6
- D.10
Show answer and solution
Correct option: C
Solution
Factor: 3sin²x - 7sinx + 2 = (3sinx - 1)(sinx - 2) = 0
sinx = 2 is impossible, so sinx = 1/3.
In [0, 2π], sinx = 1/3 gives exactly 2 solutions (one in first quadrant, one in second quadrant). In [0, 5π], there are two complete periods [0, 4π] giving 4 solutions, plus one more period [4π, 5π] which covers [0, π], giving 2 more solutions (since 1/3 > 0, both solutions in (0, π) fit within [4π, 5π]).
Total = 4 + 2 = 6.
sinx = 2 is impossible, so sinx = 1/3.
In [0, 2π], sinx = 1/3 gives exactly 2 solutions (one in first quadrant, one in second quadrant). In [0, 5π], there are two complete periods [0, 4π] giving 4 solutions, plus one more period [4π, 5π] which covers [0, π], giving 2 more solutions (since 1/3 > 0, both solutions in (0, π) fit within [4π, 5π]).
Total = 4 + 2 = 6.
[1998]