Question

How do you find the exact value of `(sin30)^2+(cos30)^2`?

Answer 1

The expression equals `1`.

Explanation:

Consider the special triangle below.

We start by defining sine and cosine. `sintheta = "opposite"/"hypotenuse"` and `costheta = "adjacent"/"hypotenuse"`. We use the special triangle above to apply the ratio to the given angles.

`30˚` is opposite the side measuring `1` and adjacent the side measuring `sqrt(3)`. The triangle has a hypotenuse of `2`.

So, `sin30˚ = 1/2` and `cos30˚= sqrt(3)/2`.

We can now calculate the value of `(sin30)^2 + (cos30)^2`.

`(sin30˚)^2 + (cos30˚)^2 = (1/2)^2 + (sqrt(3)/2)^2 = 1/4 + 3/4 = 4/4 = 1`

Note that we could also have used the pythagorean identity `sin^2theta+ cos^2theta = 1` to solve this problem.

Hopefully this helps!