Question

If `tanB=3` what is `sinB`?

Answer 1

Assuming you want your answer without the use of a calculator, `sinB=3cosB`

Explanation:

`tanB=3`

`sinB/cosB=3`

`sinB=3cosB`

But `cosB=1/(sqrt(1+tan^2B))=1/sqrt10`

`sinB=3/sqrt10=3/10sqrt10`

Answer 2

We know that `tantheta = ("side opposite "theta)/("side adjacent "theta)`

So, the side opposite `B` measures `3` and the side adjacent `B` measures `1`.

We now find the length of the hypotenuse of the imaginary triangle:

`3^2 + 1^2 = h^2`

`9 + 1 = h^2`

`h = sqrt10`

We now apply the definition that `sintheta = ("side opposite "theta)/("hypotenuse")`.

Therefore, `sintheta = 3/sqrt(10) = (3sqrt(10))/10`.

Hopefully this helps!