Question

Daca x apartine(0,90 grade) si sinx=5 pe 13 Calculați sin2x

Answer 1

cu formula fundamentla a trigonometriei ai imediat cosx= +-12/13
 pt ca
x apartine(0,90 grade) , cos x=12/13
 atunci sin2x=2sinxcosx=2*(5/13)*(12/13)=120/169

Answer 2

   
[tex]\displaystyle\\ \text{Folosim formulele: } \\\\ \cos\alpha = \sqrt{1-\sin^2 \alpha} \\ \sin 2\alpha = 2\sin\alpha\cos\alpha\\\\ \text{Rezolvare:}\\\\ \sin x = \frac{5}{13} \\\\ \sin 2x = 2\sin x \cos x = 2\sin x \sqrt{1-\sin^2 x} = 2\cdot \frac{5}{13} \cdot \sqrt{1- \Big(\frac{5}{13}\Big)^2 }=\\\\ =2\cdot \frac{5}{13} \cdot \sqrt{1- \frac{25}{169} }=2\cdot \frac{5}{13} \cdot \sqrt{\frac{169-25}{169} }=2\cdot \frac{5}{13} \cdot \sqrt{\frac{144}{169} }= [/tex]

[tex]\displaystyle\\ =2\cdot \frac{5}{13} \cdot \frac{12}{13} =\frac{2\cdot5\cdot12}{13^2}=\boxed{\frac{120}{169}}[/tex]