三角函數(shù)題目及答案

一、單項選擇題（總共10題，每題2分）1.函數(shù)f(x)=sin(x)+cos(x)的最小正周期是A.πB.2πC.π/2D.4π答案：B2.函數(shù)f(x)=sin(2x)+cos(3x)的周期是A.2πB.πC.3π/2D.π/2答案：B3.函數(shù)f(x)=sin(x)cos(x)的周期是A.πB.2πC.π/2D.4π答案：A4.函數(shù)f(x)=sin^2(x)的周期是A.πB.2πC.π/2D.4π答案：A5.函數(shù)f(x)=sin(x)+cos(2x)的最小正周期是A.πB.2πC.π/2D.4π答案：B6.函數(shù)f(x)=sin(x)cos(2x)的周期是A.πB.2πC.π/2D.4π答案：B7.函數(shù)f(x)=sin(3x)+cos(4x)的最小正周期是A.πB.2πC.π/2D.4π答案：B8.函數(shù)f(x)=sin(x)+sin(2x)的周期是A.πB.2πC.π/2D.4π答案：B9.函數(shù)f(x)=sin^2(x)+cos^2(x)的周期是A.πB.2πC.π/2D.4π答案：B10.函數(shù)f(x)=sin(x)+cos(x)的周期是A.πB.2πC.π/2D.4π答案：B二、多項選擇題（總共10題，每題2分）1.下列函數(shù)中，周期為π的函數(shù)有A.sin(x)B.cos(x)C.sin(2x)D.cos(2x)答案：A,B,C,D2.下列函數(shù)中，周期為2π的函數(shù)有A.sin(x)B.cos(x)C.sin(2x)D.cos(2x)答案：A,B,D3.下列函數(shù)中，周期為π/2的函數(shù)有A.sin(2x)B.cos(2x)C.sin(4x)D.cos(4x)答案：A,B,C,D4.下列函數(shù)中，周期為4π的函數(shù)有A.sin(x)B.cos(x)C.sin(2x)D.cos(2x)答案：A,B,C,D5.下列函數(shù)中，周期為π的函數(shù)有A.sin(x)B.cos(x)C.sin(3x)D.cos(3x)答案：A,B,C,D6.下列函數(shù)中，周期為2π的函數(shù)有A.sin(x)B.cos(x)C.sin(4x)D.cos(4x)答案：A,B,D7.下列函數(shù)中，周期為π/2的函數(shù)有A.sin(2x)B.cos(2x)C.sin(6x)D.cos(6x)答案：A,B,C,D8.下列函數(shù)中，周期為4π的函數(shù)有A.sin(x)B.cos(x)C.sin(5x)D.cos(5x)答案：A,B,C,D9.下列函數(shù)中，周期為π的函數(shù)有A.sin(x)B.cos(x)C.sin(7x)D.cos(7x)答案：A,B,C,D10.下列函數(shù)中，周期為2π的函數(shù)有A.sin(x)B.cos(x)C.sin(8x)D.cos(8x)答案：A,B,D三、判斷題（總共10題，每題2分）1.函數(shù)f(x)=sin(x)+cos(x)的周期是π。A.正確B.錯誤答案：B2.函數(shù)f(x)=sin(2x)+cos(3x)的周期是2π。A.正確B.錯誤答案：A3.函數(shù)f(x)=sin(x)cos(x)的周期是π。A.正確B.錯誤答案：A4.函數(shù)f(x)=sin^2(x)的周期是2π。A.正確B.錯誤答案：B5.函數(shù)f(x)=sin(x)+cos(2x)的周期是π。A.正確B.錯誤答案：B6.函數(shù)f(x)=sin(x)cos(2x)的周期是2π。A.正確B.錯誤答案：A7.函數(shù)f(x)=sin(3x)+cos(4x)的周期是2π。A.正確B.錯誤答案：A8.函數(shù)f(x)=sin(x)+sin(2x)的周期是π。A.正確B.錯誤答案：B9.函數(shù)f(x)=sin^2(x)+cos^2(x)的周期是2π。A.正確B.錯誤答案：B10.函數(shù)f(x)=sin(x)+cos(x)的周期是2π。A.正確B.錯誤答案：A四、簡答題（總共4題，每題5分）1.函數(shù)f(x)=sin(x)+cos(x)的最小正周期是多少？答案：函數(shù)f(x)=sin(x)+cos(x)的最小正周期是2π。因為sin(x)和cos(x)的周期都是2π，所以它們的和的周期也是2π。2.函數(shù)f(x)=sin(2x)+cos(3x)的最小正周期是多少？答案：函數(shù)f(x)=sin(2x)+cos(3x)的最小正周期是6π。因為sin(2x)的周期是π，cos(3x)的周期是2π，它們的最小公倍數(shù)是6π。3.函數(shù)f(x)=sin(x)cos(x)的最小正周期是多少？答案：函數(shù)f(x)=sin(x)cos(x)的最小正周期是π。因為sin(x)cos(x)可以寫成(1/2)sin(2x)，而sin(2x)的周期是π。4.函數(shù)f(x)=sin^2(x)+cos^2(x)的最小正周期是多少？答案：函數(shù)f(x)=sin^2(x)+cos^2(x)的最小正周期是2π。因為sin^2(x)和cos^2(x)的周期都是π，所以它們的和的周期是2π。五、討論題（總共4題，每題5分）1.討論函數(shù)f(x)=sin(x)+cos(x)的性質(zhì)。答案：函數(shù)f(x)=sin(x)+cos(x)是一個周期函數(shù)，其最小正周期為2π。函數(shù)在區(qū)間[0,2π]內(nèi)有兩個零點，分別在x=π/4和x=5π/4。函數(shù)的最大值為√2，最小值為-√2。函數(shù)在區(qū)間[0,π/4]和[5π/4,2π]內(nèi)單調(diào)遞增，在區(qū)間[π/4,5π/4]內(nèi)單調(diào)遞減。2.討論函數(shù)f(x)=sin(2x)+cos(3x)的性質(zhì)。答案：函數(shù)f(x)=sin(2x)+cos(3x)是一個周期函數(shù)，其最小正周期為6π。函數(shù)在區(qū)間[0,6π]內(nèi)有兩個零點，分別在x=π/2和x=3π/2。函數(shù)的最大值為√2，最小值為-√2。函數(shù)在區(qū)間[0,π/2]和[3π/2,6π]內(nèi)單調(diào)遞增，在區(qū)間[π/2,3π/2]內(nèi)單調(diào)遞減。3.討論函數(shù)f(x)=sin(x)cos(x)的性質(zhì)。答案：函數(shù)f(x)=sin(x)cos(x)是一個周期函數(shù)，其最小正周期為π。函數(shù)在區(qū)間[0,π]內(nèi)有兩個零點，分別在x=0和x=π。函數(shù)的最大值為1/2，最小值為-1/2。函數(shù)在區(qū)間[0,π/2]和[π/2,π]內(nèi)單調(diào)遞增，在區(qū)間[π/2