Trigonometric identities and formulas

Apply identities and formulas under appropriate conditions and check solution ranges.

Meaning

Trigonometric formulas relate values at one or more angles. Distance on the unit circle explains A unit-circle point is (cos x, sin x) at distance 1 from the origin. The Pythagorean theorem makes the sum of its squared coordinates equal to 1, giving the identity.

Example

If and lies in the first quadrant, then and A squared relationship alone does not determine cosine's sign. Use the angle range or quadrant as well.

Practice for this concept

Scope and references

Topics

Basic identities, angle-addition formulas, double-angle formulas, trigonometric equations

Learning goal

Apply identities and formulas under appropriate conditions and check solution ranges.

Helpful background

Check trigonometric definitions and angle ranges.