新高考數(shù)學(xué)二輪復(fù)習(xí) 小題綜合練專題09 三角函數(shù)與解三角形（原卷版）

專題09三角函數(shù)與解三角形小題綜合一、單選題1．（2023·浙江金華·模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上有且僅有2個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·浙江·校聯(lián)考二模）在三角形SKIPIF1<0中，SKIPIF1<0和SKIPIF1<0分別是SKIPIF1<0邊上的高和中線，則SKIPIF1<0（

）A．14 B．15 C．16 D．173．（2023·浙江紹興·統(tǒng)考二模）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)取得一個(gè)最大值SKIPIF1<0和一個(gè)最小值SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·校考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0的最小正周期為T，且SKIPIF1<0，若SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·浙江紹興·統(tǒng)考模擬預(yù)測(cè)）若函數(shù)SKIPIF1<0的周期為SKIPIF1<0，其圖象由函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位得到，則SKIPIF1<0的一個(gè)單調(diào)遞增區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）如圖，某同學(xué)到野外進(jìn)行實(shí)踐，測(cè)量魚塘兩側(cè)的兩棵大榕樹A，B之間的距離．從B處沿直線走了SKIPIF1<0到達(dá)C處，測(cè)得SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0的部分圖象如圖所示，其中SKIPIF1<0，圖中函數(shù)SKIPIF1<0的圖象與坐標(biāo)軸的交點(diǎn)分別為SKIPIF1<0，則下列代數(shù)式中為定值的是（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2023春·浙江杭州·高三浙江省杭州第二中學(xué)校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，若存在唯一的實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2023·浙江·校聯(lián)考二模）數(shù)學(xué)里有一種證明方法叫做Proofwithoutwords，也被稱為無字證明，是指僅用圖象而無需文字解釋就能不證自明的數(shù)學(xué)命題，由于這種證明方法的特殊性，無字證時(shí)被認(rèn)為比嚴(yán)格的數(shù)學(xué)證明更為優(yōu)雅與有條理.如下圖，點(diǎn)SKIPIF1<0為半圓SKIPIF1<0上一點(diǎn)，SKIPIF1<0，垂足為SKIPIF1<0，記SKIPIF1<0，則由SKIPIF1<0可以直接證明的三角函數(shù)公式是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．（2023·浙江溫州·樂清市知臨中學(xué)?？寄M預(yù)測(cè)）在函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0中，既是奇函數(shù)又是周期函數(shù)的有（

）個(gè)A．0 B．1 C．2 D．311．（2023·浙江寧波·鎮(zhèn)海中學(xué)?？寄M預(yù)測(cè)）趙爽弦圖是中國(guó)古代數(shù)學(xué)的重要發(fā)現(xiàn)，它是由四個(gè)全等直角三角形與一個(gè)小正方形拼成的一個(gè)大正方形（如圖）．已知小正方形的面積為1，直角三角形中較小的銳角為SKIPIF1<0，且SKIPIF1<0，則大正方形的面積為（

）

A．4 B．5 C．16 D．2512．（2023·浙江·校聯(lián)考三模）在平面直角坐標(biāo)系中，角SKIPIF1<0的頂點(diǎn)在坐標(biāo)原點(diǎn)，始邊與SKIPIF1<0的非負(fù)半軸重合，將角SKIPIF1<0的終邊按逆時(shí)針旋轉(zhuǎn)SKIPIF1<0后，得到的角終邊與圓心在坐標(biāo)原點(diǎn)的單位圓交于點(diǎn)SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）定義SKIPIF1<0設(shè)函數(shù)SKIPIF1<0，可以使SKIPIF1<0在SKIPIF1<0上單調(diào)遞減的SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．（2023·浙江·高三專題練習(xí)）函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后對(duì)應(yīng)的函數(shù)是奇函數(shù)，函數(shù)SKIPIF1<0．若關(guān)于x的方程SKIPIF1<0在SKIPIF1<0內(nèi)有兩個(gè)不同的解α，β，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．（2023·浙江金華·模擬預(yù)測(cè)）已知向量SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．（2023·浙江·二模）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0的最小值（

）A．與SKIPIF1<0有關(guān)，與SKIPIF1<0有關(guān) B．與SKIPIF1<0有關(guān)，與SKIPIF1<0無關(guān)C．與SKIPIF1<0無關(guān)，與SKIPIF1<0有關(guān) D．與SKIPIF1<0無關(guān)，與SKIPIF1<0無關(guān)17．（2023·浙江金華·統(tǒng)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，集合SKIPIF1<0中恰有3個(gè)元素，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<018．（2023·浙江紹興·統(tǒng)考模擬預(yù)測(cè)）設(shè)函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0，若SKIPIF1<0，且SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，則（

）A．SKIPIF1<0 B．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱C．SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù) D．SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有兩個(gè)極值點(diǎn)19．（2023·浙江·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，若將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后得到函數(shù)SKIPIF1<0的圖象，若關(guān)于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0上有且僅有兩個(gè)不相等的實(shí)根，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上單調(diào)，則SKIPIF1<0的最大值為（

）．A．3 B．5 C．6 D．7二、多選題21．（2023·浙江溫州·樂清市知臨中學(xué)?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0，則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0的最小正周期是SKIPIF1<0B．函數(shù)SKIPIF1<0的最大值為1，最小值為SKIPIF1<0C．函數(shù)SKIPIF1<0的圖像在區(qū)間SKIPIF1<0上單調(diào)遞減D．函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0對(duì)稱22．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知向量SKIPIF1<0，則下列說法正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0B．若SKIPIF1<0為銳角，則SKIPIF1<0C．若SKIPIF1<0在SKIPIF1<0上的投影向量為SKIPIF1<0，則SKIPIF1<0D．SKIPIF1<0的最小值為1，最大值為323．（2023·浙江·校聯(lián)考三模）已知函數(shù)SKIPIF1<0，則下列判斷正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<0B．若將SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位得到奇函數(shù)，則SKIPIF1<0的最小值為SKIPIF1<0C．若SKIPIF1<0在SKIPIF1<0單調(diào)遞減，則SKIPIF1<0D．若SKIPIF1<0在SKIPIF1<0上只有1個(gè)零點(diǎn)，則SKIPIF1<024．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知SKIPIF1<0，則下列命題中成立的是（

）．A．若SKIPIF1<0，SKIPIF1<0是第一象限角，則SKIPIF1<0B．若SKIPIF1<0，SKIPIF1<0是第二象限角，則SKIPIF1<0C．若SKIPIF1<0，SKIPIF1<0是第三象限角，則SKIPIF1<0D．若SKIPIF1<0，SKIPIF1<0是第四象限角，則SKIPIF1<025．（2023·浙江·校聯(lián)考二模）已知函數(shù)SKIPIF1<0為奇函數(shù)，則參數(shù)SKIPIF1<0的可能值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<026．（2023·浙江·高三專題練習(xí)）已知函數(shù)SKIPIF1<0是SKIPIF1<0的導(dǎo)函數(shù)，則（

）A．SKIPIF1<0與SKIPIF1<0的周期相同B．SKIPIF1<0與SKIPIF1<0的值域相同C．SKIPIF1<0可能是奇函數(shù)D．SKIPIF1<0的最大值是SKIPIF1<027．（2023·浙江·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0,且圖象經(jīng)過點(diǎn)SKIPIF1<0,則(

)A．SKIPIF1<0B．點(diǎn)SKIPIF1<0為函數(shù)SKIPIF1<0圖象的對(duì)稱中心C．直線SKIPIF1<0為函數(shù)SKIPIF1<0圖象的對(duì)稱軸D．函數(shù)SKIPIF1<0的單調(diào)增區(qū)間為SKIPIF1<028．（2023·浙江·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則（

）A．若SKIPIF1<0的最小正周期為SKIPIF1<0，則SKIPIF1<0B．若SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0C．若SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0D．若SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位，得到的函數(shù)為偶函數(shù)，則SKIPIF1<0的最小值為SKIPIF1<029．（2023·浙江寧波·鎮(zhèn)海中學(xué)校考二模）將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位，得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0在SKIPIF1<0上為增函數(shù)，則SKIPIF1<0的值可能為（

）A．SKIPIF1<0 B．1 C．2 D．330．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知向量SKIPIF1<0，函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0在SKIPIF1<0上有4個(gè)零點(diǎn)B．SKIPIF1<0在SKIPIF1<0單調(diào)遞增C．SKIPIF1<0D．直線SKIPIF1<0是曲線SKIPIF1<0的一條切線三、填空題31．（2023秋·浙江紹興·高三期末）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0___________．32．（2023秋·浙江嘉興·高三統(tǒng)考期末）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有3個(gè)零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是__________.33．（2023·浙江·高三專題練習(xí)）定義在R上的非常數(shù)