Question

If Tan A=5/12 then find cot A, cos A and Sin A

Answer 1

Cot A=1/tan A=12/5

cos A= 12/13

sin A=5/13

Draw a right angled triangle

the hypotenuse is the longest side which is 13 using Pythagoras theorem

the side opposite the angle A is 5

the side closest to the angle A which is called the adjacent is 12

sinA =opp/hyp

cos A= adj/hyp

cotA =1/tanA=cos A/sinA

Note: Pythagoras theorem is

hyp²=opp²+adj²

Answer 2

Explanation:

`tan \ A = (5)/(12)=(opposite \ site)/(adjacent \ side)`

hypotenuse² = (opposite side)² + (adjacent side)²

= 5² + 12²

= 25 + 144

= 169

hypotenuse = √169 = √13*13 = 13

`Cot \ A = (adjacent \ side)/(opposite \ side)=(12)/(5)\\\\Cos \ A = (adjacent \ side)/(hypotenuse)=(12)/(13)\\\\Sin \ A = (opposite \ side)/(hypotenuse)=(5)/(13)`