 Hi and welcome to the session, I am Deepika here. Let's discuss the question if sine a is equal to 3 by 4 calculate cos a and tan a. Now we know that according to the Pythagoras theorem in triangle right angle at b square is equal to ab square plus bc square that is hypotenuse square is equal to sum of the squares of other two sides and sine a is equal to sine opposite to angle a hypotenuse is equal to adjacent to angle a hypotenuse to angle a adjacent to angle a. This is a key idea behind our question to help of this key idea to solve the questions. So let's have the solution equal to 3 upon 4 abc is of triangle right angle at b now sine a is equal to 3 by 4 it means the side opposite to angle a upon side hypotenuse is equal to 3 upon 4 that is sine a is equal to bc upon ac and this is equal to 3 by 4. So if bc is equal to 4k where k is any positive number it is a positive number. Now according to the Pythagoras theorem this is equal to ab square plus bc square is equal to that is 4k square equal to ab square plus bc square that is 4k square is equal to 16k square is equal to a b square plus 9k square. This implies 16k square minus 9k square is equal to a b square that is is equal to a b square. This implies a b is equal to root 7k. So a b is equal to root 7k. Now we want to find cos a n 10 a cos a is equal to site at the center angle a upon hypotenuse that is a b upon a c and this is equal to root 7k upon 4k which is equal to root 7 upon 4 and n a is equal to site opposite to angle a that is b c upon site adjacent to angle a a b. Now b c is 3k upon a b is root 7k. So this is equal to 3 over root 7 hence the answer for the above question is cos a is equal to root 7 upon 4 is equal to 3 upon root 7. So this is the answer for the above question. I hope the solution is clear to you. Bye and take care.