Trigonometric Functions — Class 11 Mathematics

Core Concepts

Angles may be measured in degrees or radians. The conversion is 180°=π radians. On the unit circle, trigonometric functions are defined using coordinates, which also explains their signs in different quadrants.

Worked Examples

Example: 150°=150π/180=5π/6 radians.

Example: sin(5π/6)=1/2 because the reference angle is π/6 and sine is positive in Quadrant II.

Using sin²θ+cos²θ=1, if sinθ=3/5 and θ is acute, cosθ=4/5.

Explained MCQs

1. π/3 radians equals 60°. Multiply by 180/π.
2. sinθ is negative in Quadrants III and IV.
3. The period of sin x is 2π; the graph repeats after a full cycle.

Practice

1. Convert 225° into radians.
2. Evaluate sin75° using the compound-angle formula.
3. Prove 1+tan²θ=sec²θ from sin²θ+cos²θ=1.