First slide

Trigonometric equations

Question

Number of values of $x \in [0, 4 π]$ and satisfying the equation $\sin x + \cos x = 3 / 2$ is

Moderate

A

0
B

1
C

2
D

4

Solution

$\sin x + \cos x = \sqrt{2} \sin (x + \frac{π}{4}) \leq \sqrt{2} < \frac{3}{2}$
Thus, no values of $x$

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