旋轉(zhuǎn)函數(shù)中考真題及答案

一、單項(xiàng)選擇題（總共10題，每題2分）1.下列哪個(gè)函數(shù)是旋轉(zhuǎn)函數(shù)？A.y=x^2B.y=sin(x)C.y=x^3D.y=log(x)答案：B2.函數(shù)y=cos(x)的周期是？A.πB.2πC.π/2D.4π答案：B3.函數(shù)y=tan(x)在哪個(gè)區(qū)間內(nèi)是單調(diào)遞增的？A.(0,π/2)B.(π/2,π)C.(π,3π/2)D.(3π/2,2π)答案：A4.函數(shù)y=sin(x)在x=π/2處的導(dǎo)數(shù)是？A.0B.1C.-1D.π答案：B5.函數(shù)y=cos(x)在x=π處的導(dǎo)數(shù)是？A.0B.1C.-1D.π答案：C6.函數(shù)y=tan(x)在x=π/4處的導(dǎo)數(shù)是？A.1B.-1C.0D.√2答案：D7.函數(shù)y=sin(x)+cos(x)的周期是？A.πB.2πC.π/2D.4π答案：B8.函數(shù)y=sin(2x)的周期是？A.πB.2πC.π/2D.4π答案：A9.函數(shù)y=cos(3x)的周期是？A.πB.2πC.π/3D.4π答案：C10.函數(shù)y=tan(4x)的周期是？A.π/4B.π/2C.πD.2π答案：A二、多項(xiàng)選擇題（總共10題，每題2分）1.下列哪些函數(shù)是周期函數(shù)？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=x^2答案：A,B,C2.下列哪些函數(shù)在某個(gè)區(qū)間內(nèi)是單調(diào)遞增的？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=log(x)答案：C,D3.下列哪些函數(shù)的導(dǎo)數(shù)在x=0處為1？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=x答案：A,D4.下列哪些函數(shù)的導(dǎo)數(shù)在x=π/2處為0？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=x^2答案：B,D5.下列哪些函數(shù)的周期是π？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=sin(2x)答案：C,D6.下列哪些函數(shù)的周期是2π？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=sin(x/2)答案：A,B7.下列哪些函數(shù)在x=π處取得極值？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=x^2答案：A,B8.下列哪些函數(shù)在x=π/4處取得極值？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=x^3答案：A,B,C9.下列哪些函數(shù)的導(dǎo)數(shù)在x=π/2處為負(fù)？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=x^2答案：B,C10.下列哪些函數(shù)的導(dǎo)數(shù)在x=π處為正？A.y=sin(x)B.y=cos(x)C.y=tan(x)D.y=x^3答案：A,D三、判斷題（總共10題，每題2分）1.函數(shù)y=sin(x)是奇函數(shù)。答案：正確2.函數(shù)y=cos(x)是偶函數(shù)。答案：正確3.函數(shù)y=tan(x)是奇函數(shù)。答案：正確4.函數(shù)y=sin(x)+cos(x)是偶函數(shù)。答案：錯(cuò)誤5.函數(shù)y=sin(2x)是奇函數(shù)。答案：錯(cuò)誤6.函數(shù)y=cos(3x)是偶函數(shù)。答案：正確7.函數(shù)y=tan(4x)是奇函數(shù)。答案：正確8.函數(shù)y=sin(x)的導(dǎo)數(shù)是cos(x)。答案：正確9.函數(shù)y=cos(x)的導(dǎo)數(shù)是-sin(x)。答案：正確10.函數(shù)y=tan(x)的導(dǎo)數(shù)是1+tan^2(x)。答案：正確四、簡(jiǎn)答題（總共4題，每題5分）1.簡(jiǎn)述函數(shù)y=sin(x)的周期性和單調(diào)性。答案：函數(shù)y=sin(x)是周期函數(shù)，周期為2π。在區(qū)間(0,π/2)內(nèi)單調(diào)遞增，在區(qū)間(π/2,π)內(nèi)單調(diào)遞減，在區(qū)間(π,3π/2)內(nèi)單調(diào)遞增，在區(qū)間(3π/2,2π)內(nèi)單調(diào)遞減。2.簡(jiǎn)述函數(shù)y=cos(x)的周期性和單調(diào)性。答案：函數(shù)y=cos(x)是周期函數(shù)，周期為2π。在區(qū)間(0,π)內(nèi)單調(diào)遞減，在區(qū)間(π,2π)內(nèi)單調(diào)遞增。3.簡(jiǎn)述函數(shù)y=tan(x)的周期性和單調(diào)性。答案：函數(shù)y=tan(x)是周期函數(shù)，周期為π。在區(qū)間(0,π/2)內(nèi)單調(diào)遞增，在區(qū)間(π/2,π)內(nèi)單調(diào)遞增。4.簡(jiǎn)述函數(shù)y=sin(x)+cos(x)的周期性和單調(diào)性。答案：函數(shù)y=sin(x)+cos(x)是周期函數(shù)，周期為2π。在區(qū)間(0,π/4)內(nèi)單調(diào)遞增，在區(qū)間(π/4,5π/4)內(nèi)單調(diào)遞減，在區(qū)間(5π/4,2π)內(nèi)單調(diào)遞增。五、討論題（總共4題，每題5分）1.討論函數(shù)y=sin(x)和y=cos(x)在區(qū)間[0,2π]內(nèi)的圖像特點(diǎn)。答案：函數(shù)y=sin(x)和y=cos(x)在區(qū)間[0,2π]內(nèi)的圖像都是周期為2π的波形。y=sin(x)在x=0處取值為0，在x=π/2處取值為1，在x=π處取值為0，在x=3π/2處取值為-1，在x=2π處取值為0。y=cos(x)在x=0處取值為1，在x=π/2處取值為0，在x=π處取值為-1，在x=3π/2處取值為0，在x=2π處取值為1。2.討論函數(shù)y=tan(x)在區(qū)間(0,π)內(nèi)的圖像特點(diǎn)。答案：函數(shù)y=tan(x)在區(qū)間(0,π)內(nèi)的圖像是周期為π的波形。在x=0處取值為0，在x=π/2處趨于無(wú)窮大。在區(qū)間(0,π/2)內(nèi)單調(diào)遞增，在區(qū)間(π/2,π)內(nèi)單調(diào)遞增。3.討論函數(shù)y=sin(2x)和y=cos(3x)在區(qū)間[0,2π]內(nèi)的圖像特點(diǎn)。答案：函數(shù)y=sin(2x)在區(qū)間[0,2π]內(nèi)的圖像是周期為π的波形。在x=0處取值為0，在x=π/4處取值為1，在x=π/2處取值為0，在x=3π/4處取值為-1，在x=π處取值為0，在x=5π/4處取值為1，在x=3π/2處取值為0，在x=7π/4處取值為-1，在x=2π處取值為0。函數(shù)y=cos(3x)在區(qū)間[0,2π]內(nèi)的圖像是周期為2π/3的波形。在x=0處取值為1，在x=π/6處取值為0，在x=π/3處取值為-1，在x=π/2處取值為0，在x=2π/3處取值為1，在x=π處取值為0，在x=4π/3處取值為-1，在x=3π/2處取值為0，在x=5π/3處取值為1，在x=2π處取值為0。4.討論函數(shù)y=sin(x)+cos(x)在區(qū)間[0,2π]內(nèi)的圖像特點(diǎn)。答案：函數(shù)y=sin(x)+cos(x)在區(qū)