cho cos alpha=-1/4 và pi/2
cho cos alpha=-1/4 và pi/2
By Genesis
By Genesis
Có: `π/2 < a < π => a` thuộc cung số `II`.
`=> sin a > 0 `
`tan a < 0`
`cot a < 0`
• `sin^2a+cos^2a =1`
`=> sin a = \sqrt(1-(-1/4)^2) = (\sqrt15)/4`
• `sin2a = 2sinacosa = 2. (\sqrt15)/4 . (-1/4) = -(\sqrt15)/8`
• `cos2a = cos^2a – sin^2a = (-1/4)^2 – ((\sqrt15)/4)^2 = -7/8`
$\dfrac{\pi}{2}<\alpha <\pi$
$\Rightarrow sin\alpha > 0$
$sin\alpha = \sqrt{1-cos^2\alpha}=\dfrac{\sqrt{15}}{4}$
$sin2\alpha= 2sin\alpha.cos\alpha=\dfrac{-\sqrt{15}}{8}$
$cos2\alpha= cos^2\alpha-sin^2\alpha=-\dfrac{7}{8}$