3.7 Trigonometric Equations

Group terms: $(\sin 6x + \sin 2x) - \sin 4x = 0$ .
Apply Sum-to-Product: $2 \sin 4x \cos 2x - \sin 4x = 0$ .
Factor: $\sin 4x (2 \cos 2x - 1) = 0$ .
Case 1: $\sin 4x = 0 \implies 4x = n\pi \implies x = \frac{n\pi}{4}$ .
Case 2: $\cos 2x = \frac{1}{2} = \cos \frac{\pi}{3}$ . $2x = 2n\pi \pm \frac{\pi}{3} \implies x = n\pi \pm \frac{\pi}{6}$ .
General Solution: $x = \frac{n\pi}{4} \cup n\pi \pm \frac{\pi}{6}$ .

Operation

Angle

Unit

Standard Values:

sin 0 = 0, sin 30 = 0.5, sin 45 = 0.707, sin 60 = 0.866, sin 90 = 1

cos 0 = 1, cos 30 = 0.866, cos 45 = 0.707, cos 60 = 0.5, cos 90 = 0

Select an operation and enter values.