三角函数知识点
1．角度制与弧度制的互化：![](https://wkrtcs.bdimg.com/rtcs/image?w=75&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"75","h":"24","dataType":"gif","c":"word/media/image1.png"})
1rad＝![](https://wkrtcs.bdimg.com/rtcs/image?w=23&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"23","h":"31","dataType":"gif","c":"word/media/image3.png"})
°≈57.30°=57°18ˊ． 1°＝≈0.01745（rad）
2.弧长及扇形面积公式
弧长公式：![](https://wkrtcs.bdimg.com/rtcs/image?w=52&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"52","h":"27","dataType":"gif","c":"word/media/image5.png"})
扇形面积公式:S=
![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"16","h":"15","dataType":"gif","c":"word/media/image7.png"})
----是圆心角且为弧度制。 r-----是扇形半径
3.任意角的三角函数
设是一个任意角，它的终边上一点p（x,y）, r=
(1)正弦sin= 余弦cos= 正切tan=
(2)各象限的符号：
![](https://wkrtcs.bdimg.com/rtcs/image?w=541&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"541","h":"127","dataType":"gif","c":"word/media/image12.png"})
sin cos tan
![](https://wkrtcs.bdimg.com/rtcs/image?w=125.4&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"125.4","h":"133.73333333333","dataType":"png","c":"word/media/image13_1.png","imgOriW":211,"imgOriH":225})
4、三角函数线
正弦线：MP; 余弦线：OM; 正切线： AT.
5.同角三角函数的基本关系：
（1）平方关系：sin2![](https://wkrtcs.bdimg.com/rtcs/image?w=15&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"15","h":"15","dataType":"gif","c":"word/media/image14.png"})
+ cos2=1。
（2）商数关系：![](https://wkrtcs.bdimg.com/rtcs/image?w=41&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"41","h":"41","dataType":"gif","c":"word/media/image15.png"})
=tan（）
6.诱导公式：奇变偶不变，符号看象限
![](https://wkrtcs.bdimg.com/rtcs/image?w=157&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"157","h":"27","dataType":"gif","c":"word/media/image17.png"})
，，．
![](https://wkrtcs.bdimg.com/rtcs/image?w=155&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"155","h":"27","dataType":"gif","c":"word/media/image20.png"})
，，．
![](https://wkrtcs.bdimg.com/rtcs/image?w=139&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"139","h":"27","dataType":"gif","c":"word/media/image23.png"})
，，．
![](https://wkrtcs.bdimg.com/rtcs/image?w=143&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"143","h":"27","dataType":"gif","c":"word/media/image26.png"})
，，．
![](https://wkrtcs.bdimg.com/rtcs/image?w=149&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"149","h":"45","dataType":"gif","c":"word/media/image29.png"})
，．
![](https://wkrtcs.bdimg.com/rtcs/image?w=151&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"151","h":"45","dataType":"gif","c":"word/media/image31.png"})
，．
注意：引入辅助角。asinθ＋bcosθ＝![](https://wkrtcs.bdimg.com/rtcs/image?w=65&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"65","h":"27","dataType":"png","c":"word/media/image39_1.png","imgOriW":1568,"imgOriH":640})
sin(θ＋)，这里辅助角所在象限由a、b的符号确定，角的值由tan＝确定。
8正弦函数、余弦函数和正切函数的图象与性质
![](https://wkrtcs.bdimg.com/rtcs/image?w=543&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"543","h":"437","dataType":"png","c":"word/media/image42.png","imgOriW":554,"imgOriH":305})
![](https://wkrtcs.bdimg.com/rtcs/image?w=551&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"551","h":"333","dataType":"png","c":"word/media/image43.png","imgOriW":585,"imgOriH":328})
9.三角函数的伸缩变化
先平移后伸缩
![](https://wkrtcs.bdimg.com/rtcs/image?w=52&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"52","h":"20","dataType":"gif","c":"word/media/image44.png"})
的图象
得![](https://wkrtcs.bdimg.com/rtcs/image?w=81&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"81","h":"20","dataType":"gif","c":"word/media/image46.png"})
的图象
得![](https://wkrtcs.bdimg.com/rtcs/image?w=91&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"91","h":"20","dataType":"gif","c":"word/media/image48.png"})
的图象
得![](https://wkrtcs.bdimg.com/rtcs/image?w=103&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"103","h":"20","dataType":"gif","c":"word/media/image50.png"})
的图象
得![](https://wkrtcs.bdimg.com/rtcs/image?w=112&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"112","h":"20","dataType":"gif","c":"word/media/image52.png"})
的图象．
先伸缩后平移
的图象
得![](https://wkrtcs.bdimg.com/rtcs/image?w=63&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"63","h":"20","dataType":"gif","c":"word/media/image54.png"})
的图象
得![](https://wkrtcs.bdimg.com/rtcs/image?w=79&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"79","h":"20","dataType":"gif","c":"word/media/image56.png"})
的图象
得![](https://wkrtcs.bdimg.com/rtcs/image?w=111&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"111","h":"20","dataType":"gif","c":"word/media/image58.png"})
的图象得的图象．
10．正弦定理 ：
![](https://wkrtcs.bdimg.com/rtcs/image?w=175&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"175","h":"41","dataType":"gif","c":"word/media/image61.png"})
.
11.余弦定理：
![](https://wkrtcs.bdimg.com/rtcs/image?w=152&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"152","h":"21","dataType":"gif","c":"word/media/image62.png"})
;
![](https://wkrtcs.bdimg.com/rtcs/image?w=152&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"152","h":"21","dataType":"gif","c":"word/media/image63.png"})
;
![](https://wkrtcs.bdimg.com/rtcs/image?w=155&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"155","h":"21","dataType":"gif","c":"word/media/image64.png"})
.
12.三角形面积定理.![](https://wkrtcs.bdimg.com/rtcs/image?w=248&md5sum=66fc449ffb646ddb3704f0b42e71ef9a&sign=cf636964f2&rtcs_flag=1&rtcs_ver=3.8&l=webapp&bucketNum=52&ipr={"t":"img","w":"248","h":"41","dataType":"gif","c":"word/media/image65.png"})
.
本文来源：https://www.2haoxitong.net/k/doc/c0d256f684868762cbaed52f.html
文档为doc格式