sin²x + cos²x = 1

Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 1 of 48.

Take 37°. Square its sine and its cosine, then add: 0.3622 + 0.6378 = 1. At 200°: 0.1170 + 0.8830 = 1. Always exactly 1.

$The circle of radius 1 with the point (cos x, sin x) and the right triangle under it$

The point ( $\cos\left(x\right)$ , $\sin\left(x\right)$ ) is 1 from the centre. Pythagoras gives

${\sin\left(x\right)}^{2}+{\cos\left(x\right)}^{2} = 1$

An equation that is true at every angle is an identity. You can swap one side for the other.

Challenge

Show that $7{\cos\left(x\right)}^{2}+7{\sin\left(x\right)}^{2}$ is 7 at every angle. Rewrite it until it reads 7.

Then press Check.

Try it yourself

7\cos^{2} x+7\sin^{2} x

Rewrite as $7$

All lessons in Trig Identities

1Identities on the Circle

4Even, Odd and Cofunctions

7Double-Angle Formulas

10Final Challenges

2Reciprocal and Quotient

5Proving Identities

8Half Angles, Power Reduction

3Pythagorean Identities

6Sum and Difference

9Product to Sum