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lianadyusmetova
@lianadyusmetova
July 2022
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Найдите 3cosα,если sinα=-(2√2)/3 и α ϵ (3π/2;2π).
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lara164
Verified answer
Sinα = -(2√2)/3 ⇒ sin²α = (-(2√2)/3)² = 8/9
sin²α + cos²α = 1 ⇒ cos² α = 1-sin²α ⇒cos²α = 1-8/9 = 1/9
cosα = √1/9 = 1/3 ( cosα = - 1/3 -не подходит для
α ϵ (3π/2;2π))
3 cos
α = 3*1/3 = 1
ответ: 1
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Answers & Comments
Verified answer
Sinα = -(2√2)/3 ⇒ sin²α = (-(2√2)/3)² = 8/9sin²α + cos²α = 1 ⇒ cos² α = 1-sin²α ⇒cos²α = 1-8/9 = 1/9
cosα = √1/9 = 1/3 ( cosα = - 1/3 -не подходит для α ϵ (3π/2;2π))
3 cosα = 3*1/3 = 1
ответ: 1