Question

If tan0 = 12/5 and cos0 = -5/13, then what is sin0

Answer 1

Question:

if tan
`\theta` = 12/5 and cos
`\theta` = -5/13, then what is sin
`\theta`

Answer:

`sin \theta = ( -12)/(13)`

Explanation:

Given:

tan
`\theta` = 12/5

cos
`\theta` = -5/13

To find:

sin
`\theta` = ?

Solution:

We can find the sin
`\theta` value by using the tan ratio and cosine ratio

`cos = ( adjacent )/(hypotenuse) = ( -5)/(13)`

`sin = ( opposite)/(hypotenuse)`

`sin \theta = tan \theta * cos\theta`

`sin \theta = (opposite)/(adjacent) * (adjacent)/(hypotenuse)` =
`( opposite)/(hypotenuse)`

On substituting the values,

`sin \theta = ( 12)/(5) * (-5)/(13)`

`sin \theta = ( -12)/(13)`