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TeroZord
@TeroZord
August 2022
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Помогите sin.cos.tg Очень надо!
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Удачник66
1) Есть формула
sin a - sin b = 2*sin(a-b)/2 * cos(a+b)/2
sin 105 - sin 15 = 2*sin 45*cos 60 = 2*√2/2*1/2 = √2/2
2) sin 3x = -√3/2
3x = (-1)^k*120 + 180*k
x = (-1)^k*40 + 60*k
3) tg^2 x + 3tg x - 4 = 0
Разложение на множители
(tg x - 1)(tg x + 4) = 0
Или через дискриминант
D = 3^2 - 4*1*(-4) = 9+16 = 25
tg x1 = (-3-5)/2 = -4; x1 = -arctg 4 + Π*k
tg x2 = (-3+5)/2 = 1; x2 = Π/4 + Π*n
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Answers & Comments
sin a - sin b = 2*sin(a-b)/2 * cos(a+b)/2
sin 105 - sin 15 = 2*sin 45*cos 60 = 2*√2/2*1/2 = √2/2
2) sin 3x = -√3/2
3x = (-1)^k*120 + 180*k
x = (-1)^k*40 + 60*k
3) tg^2 x + 3tg x - 4 = 0
Разложение на множители
(tg x - 1)(tg x + 4) = 0
Или через дискриминант
D = 3^2 - 4*1*(-4) = 9+16 = 25
tg x1 = (-3-5)/2 = -4; x1 = -arctg 4 + Π*k
tg x2 = (-3+5)/2 = 1; x2 = Π/4 + Π*n