 Hi and welcome to the session. I am Priyanka and let us discuss the following question together. It says find the values of other five trigonometric functions when value of cot x is given to us as 3 by 4. And also it is given to us that x lies in the third quadrant. So let us start with our solution. Here the value of cot x is given to us as 3 by 4. So therefore tan x value will be 1 divided by cot x that is 4 by 3. According to one of the identities that is known to us it says 1 plus tan square x is equal to 6 square x, right? So on substituting the value of tan x in this formula we have 1 plus 4 by 3 the whole square is equal to 6 square x that gives us 1 plus 16 by 9 is equal to 6 square x, 25 by 9 square root is equal to 6x that gives us the value as plus minus 5 by 3 as 6x. As we know that it lies the value of x lies in the third quadrant so that means sec x is equal to minus 5 by 3. Now we have got the value of sec x so cos x will be 1 divided by sec x that is minus 3 by 5. Proceeding on finding out further we know that sin x is equal to tan x cos x. So we have the value of tan x as 4 by 3 cos x as minus 3 by 5 and hence its value come out to be minus 4 by 5 cos x comes out to be minus 5 by 4. So this completes the question that was given to us let me write the answer together. So therefore the solution is tan x is equal to 4 by 3 sec x is equal to minus 5 by 3 cos x is equal to minus 3 by 5 cos x is equal to minus 5 by 4. And lastly sin x is equal to minus 4 by 5. Right so this completes the question that was given to us I hope you enjoyed the session bye for now.