 Hello and welcome to this session. In this session, we will discuss symmetry, even and error of trigonometric functions and also their priority with the help of unit circle. First of all, let us discuss even and all trigonometric functions. Now a function f of x is an even function x is equal to f of x. Function f of x is all function if f of minus x is equal to minus f of x. Now using these results, we will find symmetry of trigonometric functions. Now we know when we move in counterclockwise direction, the angle is positive and when we move in clockwise direction, the angle will be negative. Unit circle on the coordinate plane p be a point with coordinate 1 0 lying on circle on x axis. Now let us move the point p in anti-clockwise direction angle theta which is equal to d v v h point m. Now m is in first quadrant, so coordinates of point m are x y. Now again, move the point p in clockwise direction by same angle measure and we reach point m dash will be taken as theta is equal to minus t because in clockwise direction and the point m dash lies in fourth quadrant. So its coordinates will be x minus y on unit circle has coordinates cos theta sin theta. Now let us find the coordinates of m dash in fourth quadrant in terms of trigonometric ratios. Now where theta is equal to minus t of minus t is equal to x which is equal to, so cos will also be positive, sin of minus t is equal to minus y equal to minus is negative also be negative. Now tan of minus t is equal to minus y upon x which is equal to minus t is equal to x upon minus y which is equal to minus cos of t point of minus t is equal to 1 upon x which is equal to t is equal to 1 upon minus y which is equal to 1 upon minus is an even function if f of minus x is equal to f of function if f of minus x is equal to minus f of x. Now here you can see some functions. Thus, when f of minus t is equal to minus sin of minus t is equal to cos t equal to c can t equal to minus cos is equal to minus cos t. Thus, sin of minus 2 minus sin of minus 1 by 2 is equal to x which is equal to rule 3 by 2. Now let us discuss periodicity using unit circle. A periodic function is a function that reveals its value in all periods. Thus, a constant capital t is a period of a function at the home is equal to end with the help of unit circle values of cos theta and while coordinates give values of sin theta. Now let us try the value of cos is 1 here are different to pi. The values of cos are negative for different values of theta. For equivalent, there is no repetition of values but when we completed one revolution and reached for example if we take theta is equal to 13 pi by 6 then cos theta is equal to cos of 13 which is equal to cos of 12 pi upon 6 plus pi upon 6 which is equal to cos and reach the same point where the value the value is repeating sin theta of theta is equal to 2 pi and period of sin theta is equal to 2 pi. Now let us see period of tan theta are positive are negative tan 0. There is no repetition of values the values of tan theta are positive and same as in the first program also the value and first problem the values are sin that is the values repeating is equal to is equal to tan theta. So in this session we have discussed the way of periodicity with the help of unit circle and this completes our session hope you all have enjoyed the session.