Home > Trigonometry > Double Angle Identities

How do you simplify #\sin ^{2}(\Theta )+\cos ^{2}(\Theta )#?

Answer 1

See below.

As we know, in a circle with radius #r# the point #x,y# in the circumference obeys #sin theta = y/r# and #cos theta = x/r# with #r = sqrt(x^2+y^2)# so

#sin^2theta+cos^2theta = (y/r)^2+(x/r)^2 = (x^2+y^2)/(x^2+y^2) = 1#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Oliver Atkinson

( \sin^2(\Theta) + \cos^2(\Theta) ) simplifies to 1. This is one of the fundamental trigonometric identities known as the Pythagorean identity, which states that for any angle ( \Theta ), the square of the sine plus the square of the cosine is always equal to 1.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.