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nataevgeniy
@nataevgeniy
August 2022
2
17
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Найти корни уравнения sin(15*+x)+sin(45*-x)=1 на промежутке[0;90*]
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Verified answer
Формула "сумма синусов"
2*sin(30°)*cos(15°-x) = 1
sin(30°) = 0.5
осталось: cos(15°-x) = 1
15°-x = 0° это на
промежутке[0;90
°
]
х = 15
°
х = π/12 (в радианах)
2 votes
Thanks 1
sedinalana
2sin[(15+x+45-x)/2]*cos[(15+x-45+x)/2]=1
2sin30*cos(x-15)=1
2*1/2*cos(x-15)=1
cos(x-15)=1
x-15=360k
x=15+360k,k∈z
0≤15+360k≤90
-15≤360k≤75
-15/360≤k≤75/360
k=0⇒x=15
1 votes
Thanks 1
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Answers & Comments
Verified answer
Формула "сумма синусов"2*sin(30°)*cos(15°-x) = 1
sin(30°) = 0.5
осталось: cos(15°-x) = 1
15°-x = 0° это на промежутке[0;90°]
х = 15°
х = π/12 (в радианах)
2sin30*cos(x-15)=1
2*1/2*cos(x-15)=1
cos(x-15)=1
x-15=360k
x=15+360k,k∈z
0≤15+360k≤90
-15≤360k≤75
-15/360≤k≤75/360
k=0⇒x=15