Question

How do you sketch the angle whose terminal side in standard position passes through `(1,sqrt3)` and how do you find sin and cos?

Answer 1

`sin(x) = y/(Hyp) = sqrt(3)/2` and `cos(x)=x/(Hyp) = 1/2`

Explanation:

If you place the triangle on a graph, with one side laying on the positive side of the x-axis, and set the other side to pass through the origin and the given point `(1, sqrt(3))` it will form a right triangle.

The bottom side will be the "adjacent" side to the angle, while the vertical side is the "opposite."

knowing the acronym SOH CAH TOA
`sin=(Opposite)/(Hypotenuse)` , `cos=(Adjacent)/(Hypotenuse)` , `tan=(Opposite)/(Adjacent)`

and the Pythagorean Theorem
`(Hypotenuse)^2 = (Opposite)^2 + (Adjacent)^2`

We can find that
`Hyp^2 = (sqrt(3))^2 + 1^2`
By solving for Hyp, we see that the hypotenuse is 2 units long.

Knowing this, we can then solve the sine and cosine.