Pythagorean Identity SL

In this page, we will will learn about the Pythagorean Identities. It is actually quite rare that exam questions are solely about these identities, but it is essential that you can use and manipulate them confidently because they are used in so many different parts of the course (so they do come up a lot!). You will learn what they are and how to use them.


Key Concepts

On this page, you should learn about 

  • the Pythagorean identity  \(\large \cos^{ 2 }\theta +\sin^{ 2 }\theta \equiv 1\)

Summary

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Test Yourself

This quiz is about the Pythagorean Identity sin²x + cos²x \(\equiv\) 1


START QUIZ!

Exam-style Questions

Question 1

a) Show that the equation \(\large 2 \sin^2x=3 \cos x\) may be written in the form

\(\large 2 \cos^2x+3 \cos x-2=0\)

b) Hence, solve \(\large 2 \sin^2x=3 \cos x\) , for \(\large 0\le x\le2\pi\)

Hint

Full Solution

Question 2

 

Given that \(x=\frac{2}{cos\theta}\) and \(y=3tan\theta\)

show that \(\frac{x^2}{4}-\frac{y^2}{9}=1\)

Hint

Full Solution

Question 3

The following diagram shows triangle ABC with AB = 4 and AC = 5

DIAGRAM NOT TO SCALE

a) Given that \(\large \sin \hat A=\frac{3}{4}\), find the value of \(\large \cos \hat A\)

b) Hence, show that the length of \(\large BC=\sqrt{41-10\sqrt{7}}\)

Hint

Full Solution

Question 4

Prove that \(\large \frac{\sin ^3\theta}{\tan \theta}+\cos^3\theta\equiv\cos\theta\)

Hint

Full Solution

MY PROGRESS

How much of Pythagorean Identity SL have you understood?