Geoduom dann \( 8^{\circ} \) \( 2|\cos x|=\sqrt{3} \)

Ooh, let's dive into solving the equation \( 2|\cos x|=\sqrt{3} \). First, divide both sides by 2 to get \( |\cos x| = \frac{\sqrt{3}}{2} \). Now, we know that the cosine function is positive in the first and fourth quadrants, so we can have two cases: 1. \( \cos x = \frac{\sqrt{3}}{2} \) which gives us principal values \( x = 30^{\circ} + n \cdot 360^{\circ} \) for any integer \( n \). 2. \( \cos x = -\frac{\sqrt{3}}{2} \) giving us solutions \( x = 150^{\circ} + n \cdot 360^{\circ} \) and \( x = 210^{\circ} + n \cdot 360^{\circ} \). Now we can find the angles relative to \( 8^{\circ} \)! --- For real-world application, understanding cosines and their properties is crucial, especially in physics and engineering. They help in analyzing waves, light, and even electrical circuits! Moreover, trigonometry plays a pivotal role in computer graphics. When creating 3D models or animations, cosine functions help determine angles and positions, allowing for smooth and realistic movements. Keep those angles in mind; they’re more important than you think!