Question

Find cot 0 if cos 0=3/13

Answer 1

3/4 root 10
you make a right triangle. use Pythagorean theorem. and find the opposite side. then reduce the radical of 160. and do tan and then flip them around to make cot.

Answer 2

The value of:

`\cot \theta=(3)/(4√(10))`

Explanation:

We are given,

`\cos \theta=(3)/(13)`

We know that cos θ is the ratio of base and hypotenuse of a right angled triangle corresponding to θ.

On applying Pythagorean Theorem in ΔABC we get:

`13^2=3^2+a^2\\\\\\i.e.\\\\\\169=9+a^2\\\\\\a^2=160\\\\\\i.e.\\\\\\a=4√(10)`

Hence, the value of
`\cot \theta` is defined as the ratio of base to perpendicular length of the triangle.

Hence,

`\cot \theta=(3)/(4√(10))`