Trigonometrijas formulas — teorija. Matemātika, 11. klase.

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MATEMĀTIKĀ 3. KLASEI

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Trigonometrijas formulas matemātikas eksāmena formulu lapā

\begin{array}{l} \sin^{2} α + \cos^{2} α = 1 \\ tg α = \frac{\sin α}{\cos α} ctg α = \frac{\cos α}{\sin α} \\ 1 + {tg}^{2} α = \frac{1}{\cos^{2} α} \\ 1 + {ctg}^{2} α = \frac{1}{\sin^{2} α} \\ tg α \cdot ctg α = 1 \\ \sin 2 α = 2 \sin α \cdot \cos α \\ \cos 2 α = \cos^{2} α - \sin^{2} α \\ tg 2 α = \frac{2 tg α}{1 - {tg}^{2} α} \\ \sin (α \pm β) = \sin α \cos β \pm \cos α \sin β \\ \cos (α + β) = \cos α \cos β - \sin α \sin β \\ \cos (α - β) = \cos α \cos β + \sin α \sin β \\ tg (α + β) = \frac{tg α + tg β}{1 - tg α \cdot tg β} \\ tg (α - β) = \frac{tg α - tg β}{1 + tg α \cdot tg β} \end{array}

\begin{array}{l} \sin α + \sin β = 2 \sin \frac{α + β}{2} \cdot \cos \frac{α - β}{2} \\ \sin α - \sin β = 2 \sin \frac{α - β}{2} \cdot \cos \frac{α + β}{2} \\ \cos α + \cos β = 2 \cos \frac{α + β}{2} \cdot \cos \frac{α - β}{2} \\ \cos α - \cos β = - 2 \sin \frac{α + β}{2} \cdot \sin \frac{α - β}{2} \\ \sin α \cdot \cos β = \frac{\sin (α - β) + \sin (α + β)}{2} \\ \sin α \cdot \sin β = \frac{\cos (α - β) - \cos (α + β)}{2} \\ \cos α \cdot \cos β = \frac{\cos (α - β) + \cos (α + β)}{2} \end{array}

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3. Trigonometrijas formulas