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

1 Answer
Noah G
Nov 4, 2016

The expression equals 1.

Explanation:

Consider the special triangle below.

![http://www.sparknotes.com/math/geometry2/specialtriangles/section4.rhtml](useruploads.socratic.org)

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!

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