∡α - jest ostry ⇒ wartości wszystkich funkcji trygonometrycznych są dodatnie.
[tex]tg\alpha =2~~\land ~~tg\alpha =\dfrac{sin\alpha }{cos\alpha } ~~\Rightarrow ~~\dfrac{sin\alpha }{cos\alpha } =2\\\\\dfrac{sin\alpha }{cos\alpha } =2~~\mid \cdot ~~cos\alpha \\\\sin\alpha =2cos\alpha ~~\mid \div ~~2 \\\\cos\alpha =\dfrac{1}{2} sin\alpha \\\\\\sin^{2} \alpha =?\\\\sin^{2} \alpha +cos^{2} \alpha =1~~\land~~cos\alpha =\dfrac{1}{2} sin\alpha \\\\sin^{2} \alpha +( \dfrac{1}{2} sin\alpha) ^{2} =1\\\\sin^{2} \alpha +\dfrac{1}{4} sin^{2} \alpha =1[/tex]
[tex]1\dfrac{1}{4} sin^{2} \alpha =1\\\\\dfrac{5}{4} sin^{2} \alpha =1~~\mid \div~~\dfrac{5}{4} \\\\sin^{2} \alpha =\dfrac{4}{5}\\\\sin^{2} \alpha =0,8[/tex]
Odp: Wartość wyrażenia sin²α wynosi 0,8.
