00:01
Hello everyone, so here x is equal to 2 cos theta and y is equals to sine 2 theta.
00:15
So now d x over d t d theta will be minus 2 sine theta and dy y over d theta will be cos 2 theta multiplied by 2.
00:33
So now the slope of tangent is m is equals to d .y divided by d theta, whole divided by dx divided by d theta.
00:46
2 cos 2 theta divided by minus 2 sine theta.
00:55
So this we can also write it as minus cos 2 theta divided by sine theta so the horizontal tangent m is equal to 0 this means minus cos 2 theta divided by sine theta is equal to 0 right so if cos 2 theta is equal to 0 this means cos 2 theta is equal to cos pi divided by 2 so we can say that 2 theta is equal to to n pi plus or minus pi divided by 2.
01:45
So, theta is equal to n pi plus or minus pi divided by 4.
01:51
For n is equal to 0, theta is equals to plus or minus pi divided by 4.
02:00
So from here, we can write x is equal to 2 cos plus or minus pi divided by 4, which is root 2 and y is equal to sine 2 multiplied by plus or minus pi divided by 4 which is plus or minus 1.
02:27
So now x comma y is equal to root 2 .1 minus 1 and 2 .1 right? so this is for the horizontal tangent...