Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

In this lesson, we will learn how to derive the Pythagorean identities and solve proofs problems.

Q1:

The lengths of the sides of the right triangle shown in the figure are 3, 4, and 5. Find the areas of the squares on the three sides, and find a relationship between them.

Q2:

Consider the identity s i n c o s 2 2 π + π = 1 . We can use this to derive two new identities.

First, divide both sides of the identity by s i n 2 π to find an identity in terms of c o t π and c o s e c π .

Now, divide both sides of the identity through by c o s 2 π to find an identity in terms of t a n π and s e c π .

Q3:

The figure shows a unit circle and a radius with the lengths of its π₯ - and π¦ -components. Use the Pythagorean theorem to derive an identity connecting the lengths 1, c o s π , and s i n π .

Donβt have an account? Sign Up