Question

The number of values of θ in the interval [0, 5π] satisfying the equation 3sin²θ – 7sinθ + 2 = 0 is _______

(a) 3

(b) 4

(c) 6

(d) 5

Answer 1

The correct option (c) 6

Explanation:

equation: 3sin²θ – 7sinθ + 2 = 0

∴ (3sinθ – 1)(sinθ – 2) = 0

sinθ = (1/3) or sinθ = 2 (not possible) 

∴ sinθ = (1/3)

∴ No of solution:

(a) between 0 & π → 2 

(b) between 2π & 3π → 2

(c) between 4π & 5π → 2

∴ Total number of solution = 6.