4cos^2 x - 3=0
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 May 5, 2013 #2 Hello, mgely! \(\displaystyle \text{Find all solutions on }[0,\,2\pi]\!:\;\;4\cos^2\!x - 3\:=\:0\) Click to expand... We have: .\(\displaystyle \cos^2\!x \:=\:\dfrac{3}{4} \quad\Rightarrow\quad \cos x \:=\:\pm\dfrac{\sqrt{3}}{2}\) Therefore: .\(\displaystyle x \:=\:\dfrac{\pi}{6}\!,\dfrac{5\pi}{6}\!,\dfrac{7 \pi}{6}\!, \dfrac{11\pi}{6}\)
Hello, mgely! \(\displaystyle \text{Find all solutions on }[0,\,2\pi]\!:\;\;4\cos^2\!x - 3\:=\:0\) Click to expand... We have: .\(\displaystyle \cos^2\!x \:=\:\dfrac{3}{4} \quad\Rightarrow\quad \cos x \:=\:\pm\dfrac{\sqrt{3}}{2}\) Therefore: .\(\displaystyle x \:=\:\dfrac{\pi}{6}\!,\dfrac{5\pi}{6}\!,\dfrac{7 \pi}{6}\!, \dfrac{11\pi}{6}\)
