Question

How do you find the other trigonometric functions given `sinx=3/5, cosx=4/5`?

Answer 1

`tanx= 3/4`, `cscx = 5/3`, `secx = 5/4`, `cot x = 4/3`

Explanation:

Since both sine and cosine are positive, we know `x` is in `QI`, so all of the trig functions will be positive.

We can use the fact that `tanx = sinx /cos x` to find tangent:

`tanx=(3/5)/(4/5) = 3/4`.

The other functions can be found with the reciprocal identities:

`cscx = 1/sinx = 5/3`
`secx = 1/cosx = 5/4`
`cot x = 1/tanx = 4/3`