First slide

Trigonometric equations

Question

The number of values of x in the interval $[0, 3 π]$ satisfying the equation $2 \sin^{2} x + 5 \sin x - 3 = 0$ is

Moderate

A

2
B

4
C

6
D

1

Solution

We have $(\sin x + 3) (2 \sin x - 1) = 0$
$\Rightarrow \sin x = - 3$ which is not possible
or $\sin x = 1 / 2 \Rightarrow x = π / 6, 5 π / 6, 13 π / 6, 17 π / 6$ as $x \in [0, 3 π]$

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