Task/26163684
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Вычислить sin2α,если cosα<span> = - 4/5 и </span>π < α <3π<span>/2
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</span>* * * π < α <3π/2 ⇔2 π < 2α < 3π ⇒ sin2α > 0 * * *
sin2α = 2sinα *cosα = * * * π < α <3π/2 ⇒ sinα < 0 * * *
= - 2√(1 -cos²<span>α) *cosα = -2*</span>√(1 -(- 4/5)² ) * (- 4/5) =2*√(1 -16/25) * 4/5 =
=2*√(9/25)* (4/5) = 2*(3/5)*(4/5) = 24/25 * * * (24*4)/ (25*4) =96 /100 * * *
ответ: <span>24 / 25 . * * * </span>0,96 * * *
Cos²α=1-5/9=4/9
cosα=-2/3
√5tgα=√5*√5/3:(-2/3)=-5/3*3/2=-5/2
По рисунку
![a_{1}](https://tex.z-dn.net/?f=+a_%7B1%7D+)
=1, d=2
![a_{20}](https://tex.z-dn.net/?f=+a_%7B20%7D+)
=?
![a_{30}](https://tex.z-dn.net/?f=+a_%7B30%7D+)
=?
![a_{n} = a_{1} +(n-1)*d](https://tex.z-dn.net/?f=a_%7Bn%7D+%3D+a_%7B1%7D+%2B%28n-1%29%2Ad)
подставляем
![a_{20} =1+(20-1)*2=1+19*2=1+38=39](https://tex.z-dn.net/?f=+a_%7B20%7D+%3D1%2B%2820-1%29%2A2%3D1%2B19%2A2%3D1%2B38%3D39)
![a_{30}](https://tex.z-dn.net/?f=+a_%7B30%7D+)
=1+(30-1)*2=1+29*2=1+58=59
-2*(-0,2)+3*(-5,3)=0,4+(-15,9)=0.4-15.9=-15,5
Arcsin(sin(pi/6))=pi/6 sin(pi/6)=1/2 Ответ 1/2