Mathematics 360°

Interactive Unit Circle

Explore angles, radians, and trigonometric functions in real-time

Angle (θ)

45° 0.79 rad

Trigonometric Values

sin(θ) 0.707

cos(θ) 0.707

tan(θ) 1.000

csc(θ) 1.414

sec(θ) 1.414

cot(θ) 1.000

Quick Angles

Key Trigonometric Identities

Fundamental formulas and relationships

Pythagorean Identity

sin²(θ) + cos²(θ) = 1

The most fundamental trigonometric identity, derived from the Pythagorean theorem.

Reciprocal Identities

csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)

Relationships between primary and reciprocal functions.

Quotient Identities

tan(θ) = sin(θ)/cos(θ)
cot(θ) = cos(θ)/sin(θ)

Express tangent and cotangent in terms of sine and cosine.

Even-Odd Identities

sin(-θ) = -sin(θ)
cos(-θ) = cos(θ)
tan(-θ) = -tan(θ)

Symmetry properties of trigonometric functions.

Co-function Identities

sin(90° - θ) = cos(θ)
cos(90° - θ) = sin(θ)
tan(90° - θ) = cot(θ)

Relationships between complementary angles.

Double Angle Formulas

sin(2θ) = 2sin(θ)cos(θ)
cos(2θ) = cos²(θ) - sin²(θ)
tan(2θ) = 2tan(θ)/(1 - tan²(θ))

Formulas for double angles.

Additional Resources

More tools and materials for learning

Practice Problems

Interactive exercises to test your understanding of trigonometric concepts.

Study Notes

Comprehensive notes covering all Class 9 trigonometry topics.

Video Tutorials

Step-by-step video explanations of key mathematical concepts.