(Q9)If tan A=
3
4
,then find the other trigonometric ratio of angle A.

BAC4k3k
Given tan A=
3
4

Hence tan A=Opposite side/Adjacent side=3/4

Therefore,

opposite side:adjacent side=:

For angle A,let,opposite side=BC=3k(where k is any positive number)

Adjacent side=AB=4k

Now,we have a triangle ABC (by Pythagoras theorem)

AC2=AB2+BC2

AC2=K2

AC=k=Hypotenuse

Now,we can easily write the other ratios of trigonometry

sin A=
opposite
hypotenuse
=

cos A=
adjacent
hypotenuse
=

Hence cosec A=
1
sin A
=

sec A=
1
cos A
=

cot A=
1
tan A
=