若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,则实数a的值为?f(x)=asin(x+π/4)+3sin(x-π/4)=asin(x+π/4)-3cos(x+π/4)f(x)=√(a^2+9) cos(x+π/4-φ).其中tanφ=-a/3∵f(x)是偶函数 ∴π/4-φ=Kπ(K∈Z)φ=-Kπ+π/4,tanφ=1 所以a=-3答
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 18:44:26
![若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,则实数a的值为?f(x)=asin(x+π/4)+3sin(x-π/4)=asin(x+π/4)-3cos(x+π/4)f(x)=√(a^2+9) cos(x+π/4-φ).其中tanφ=-a/3∵f(x)是偶函数 ∴π/4-φ=Kπ(K∈Z)φ=-Kπ+π/4,tanφ=1 所以a=-3答](/uploads/image/z/7307825-41-5.jpg?t=%E8%8B%A5f%28x%29%3Dasin%28x%2B%CF%80%2F4%29%2B3sin%28x-%CF%80%2F4%29%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0%2C%E5%88%99%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC%E4%B8%BA%3Ff%28x%29%3Dasin%28x%2B%CF%80%2F4%29%2B3sin%28x-%CF%80%2F4%29%3Dasin%28x%2B%CF%80%2F4%29-3cos%28x%2B%CF%80%2F4%29f%28x%29%3D%E2%88%9A%EF%BC%88a%5E2%2B9%29+cos%28x%2B%CF%80%2F4-%CF%86%29.%E5%85%B6%E4%B8%ADtan%CF%86%3D-a%2F3%E2%88%B5f%28x%29%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0+%E2%88%B4%CF%80%2F4-%CF%86%3DK%CF%80%EF%BC%88K%E2%88%88Z%EF%BC%89%CF%86%3D-K%CF%80%2B%CF%80%2F4%2Ctan%CF%86%3D1+%E6%89%80%E4%BB%A5a%3D-3%E7%AD%94)
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