![\mathtt{-1,5+3,5sin\alpha}](https://tex.z-dn.net/?f=%5Cmathtt%7B-1%2C5%2B3%2C5sin%5Calpha%7D)
, если
![\mathtt{cos\alpha=\frac{4\sqrt{3}}{7}}](https://tex.z-dn.net/?f=%5Cmathtt%7Bcos%5Calpha%3D%5Cfrac%7B4%5Csqrt%7B3%7D%7D%7B7%7D%7D)
и
![\mathtt{\alpha\in(0а;\frac{\pi}{2})}](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Calpha%5Cin%280%D0%B0%3B%5Cfrac%7B%5Cpi%7D%7B2%7D%29%7D)
вообще,
![\mathtt{sin\alpha=б\sqrt{1-cos^2\alpha}}](https://tex.z-dn.net/?f=%5Cmathtt%7Bsin%5Calpha%3D%D0%B1%5Csqrt%7B1-cos%5E2%5Calpha%7D%7D)
(всё зависит от четверти), но, так как перед нами первая четверть, то, следовательно, искомый синус будет положительным. итак,
![\mathtt{sin\alpha=\sqrt{1-(\frac{4\sqrt{3}}{7})^2}=\sqrt{1-\frac{48}{49}}=\sqrt{\frac{1}{49}}=\frac{1}{7}}}](https://tex.z-dn.net/?f=%5Cmathtt%7Bsin%5Calpha%3D%5Csqrt%7B1-%28%5Cfrac%7B4%5Csqrt%7B3%7D%7D%7B7%7D%29%5E2%7D%3D%5Csqrt%7B1-%5Cfrac%7B48%7D%7B49%7D%7D%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B49%7D%7D%3D%5Cfrac%7B1%7D%7B7%7D%7D%7D)
, и, следовательно,
![\mathtt{3,5sin\alpha-1,5=3,5*\frac{1}{7}-1,5=\frac{1}{2}-1,5=-1}](https://tex.z-dn.net/?f=%5Cmathtt%7B3%2C5sin%5Calpha-1%2C5%3D3%2C5%2A%5Cfrac%7B1%7D%7B7%7D-1%2C5%3D%5Cfrac%7B1%7D%7B2%7D-1%2C5%3D-1%7D)
5,7a^2-2,1ab+b^2-3,9ab+0,3a^2-2b^2=6a^2-6ab-b^2. подставляем значения: 6*(-1)^2-6*(-1)*5-5^2=6+30-25=11.
1/3 V 45 = V ( 1/9 • 45 ) = V 5
![cos15 = cos\dfrac{30}{2} = \sqrt{\dfrac{1 + cos30}{2}} = \sqrt{\dfrac{1 + \dfrac{\sqrt{3} }{2} }{2} } = \sqrt{\dfrac{1 + \sqrt{3} }{4}} = \dfrac{\sqrt{1 + \sqrt{3} } }{2}](https://tex.z-dn.net/?f=cos15+%3D+cos%5Cdfrac%7B30%7D%7B2%7D+%3D+%5Csqrt%7B%5Cdfrac%7B1+%2B+cos30%7D%7B2%7D%7D+%3D+%5Csqrt%7B%5Cdfrac%7B1+%2B+%5Cdfrac%7B%5Csqrt%7B3%7D+%7D%7B2%7D+%7D%7B2%7D+%7D+%3D+%5Csqrt%7B%5Cdfrac%7B1+%2B+%5Csqrt%7B3%7D+%7D%7B4%7D%7D+%C2%A0%3D+%5Cdfrac%7B%5Csqrt%7B1+%2B+%5Csqrt%7B3%7D+%7D+%7D%7B2%7D)
![sin75 = cos(90 - 75) = cos15](https://tex.z-dn.net/?f=sin75+%3D+cos%2890+-+75%29+%3D+cos15)
Ответ: sin75° = cos15° = √(1 + √3)/2