Question

How do you find `sintheta` and `costheta` if the terminal side of `theta` lies along the line `y=2x` in QI?

Answer 1

The slope, m, of the line `y = 2x` is, `m =2`.

For this line, we know that any ordered pair of coordinates will form a right triangle, therefore, we can choose any point and use the Pythagorean Theorem to compute the hypotenuse:

`h^2 = x^2+y^2`

Let's choose the point `(1,2)`:

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

`h^2 = 1+4`

`h^2 = 5`

`h = sqrt5`

We know that:

`sin(theta) = y/h`

`sin(theta) = 2/sqrt5`

Rationalize the denominator:

`sin(theta) = 2sqrt5/5`

We know that:

`cos(theta) = x/h`

`cos(theta) = 1/sqrt5`

Rationalize the denominator:

`cos(theta) = sqrt5/5`