问几道高一的数学题.^--^1.(sin1°)^2+(sin2°)^2+……+(sin89°)^2+(sin90°)^2=?的过程.2.已知函数f(x)=sin(ωx+φ) (ω>0,0
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![问几道高一的数学题.^--^1.(sin1°)^2+(sin2°)^2+……+(sin89°)^2+(sin90°)^2=?的过程.2.已知函数f(x)=sin(ωx+φ) (ω>0,0](/uploads/image/z/5323001-41-1.jpg?t=%E9%97%AE%E5%87%A0%E9%81%93%E9%AB%98%E4%B8%80%E7%9A%84%E6%95%B0%E5%AD%A6%E9%A2%98.%5E--%5E1.%28sin1%C2%B0%29%5E2%2B%28sin2%C2%B0%29%5E2%2B%E2%80%A6%E2%80%A6%2B%28sin89%C2%B0%29%5E2%2B%28sin90%C2%B0%29%5E2%3D%3F%E7%9A%84%E8%BF%87%E7%A8%8B.2.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28%CF%89x%2B%CF%86%29+%28%CF%89%3E0%2C0)
问几道高一的数学题.^--^1.(sin1°)^2+(sin2°)^2+……+(sin89°)^2+(sin90°)^2=?的过程.2.已知函数f(x)=sin(ωx+φ) (ω>0,0
问几道高一的数学题.^--^
1.(sin1°)^2+(sin2°)^2+……+(sin89°)^2+(sin90°)^2=?的过程.
2.已知函数f(x)=sin(ωx+φ) (ω>0,0
问几道高一的数学题.^--^1.(sin1°)^2+(sin2°)^2+……+(sin89°)^2+(sin90°)^2=?的过程.2.已知函数f(x)=sin(ωx+φ) (ω>0,0
1.(sin1°)^2+(sin2°)^2+…(sin88°)^2+(sin89°)^2+(sin90°)^2
=(sin²1°+sin²89°)+(sin²2°+sin²88°)+...+(sin²44+sin²46)+sin²45+sin²90°=44*1+1/2+1=45.5
注:sin45°=√2/2,sin90°=1
2.注:e代表φ
f(x)是偶函数
∴f(x)=coswx
sin(wx+π/2)=coswx
∴e=π/2
∵关于(3π/4,0)中心对称
∴f(3π/4)=cos3wπ/4=0
3wπ/4=π/2+kπ
w=2/3+4/3k
又在[0,π/2]上是单调函数
T=2π/w>2π
w<1
∴w=2/3
w=2/3
e=π/2
或者注:u代表φ
由于函数f(x)=sin(wx+u)(w>0,0≤u≤∏)是R上的偶函数,因此函数必可化为coswx,所以u=∏/2,于是f(x)=coswx
而在[0,∏/2]上是单调函数,因0=
sin1°=cos89°
(cos89°)^2+(sin89°)^2=1
所以 原等式=44+(sin45°)^2+(sin90°)^2=45+1/2
φ=π/2 ω=2