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

1 Answer
Nov 4, 2016

The expression equals #1#.

Explanation:

Consider the special triangle below.

http://www.sparknotes.com/math/geometry2/specialtriangles/section4.rhtml

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!