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Chemistry LibreTexts

16.4: Trigonometric Identities

  • Page ID
    106906
    • \(\sin^2 u + \cos^2 u = 1\)
    • \(\tan u = \frac{\sin u}{\cos u}\)
    • \(\sin \left( \frac{\pi}{2} − u \right) = \cos u\)
    • \(\cos \left( \frac{\pi}{2} − u \right) = \sin u\)
    • \(\sin (u \pm v) = \sin u \cos v \pm \cos u \sin v\)
    • \(\cos (u \pm v) = \cos u \cos v \mp \sin u \sin v\)
    • \(\sin (−u) = − \sin u\)
    • \(\cos (−u) = \cos u\)
    • \(\tan (−u) = − \tan u\)
    • \(\sin u \cos v = \frac{1}{2} \left[ \sin (u + v) + \sin (u − v) \right]\)
    • \(\sin u \sin v = \frac{1}{2} \left[ \cos (u − v) − \cos (u + v) \right]\)
    • \(\cos u \cos v = \frac{1}{2} \left[ \cos (u − v) + \cos (u + v) \right]\)
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