Q1. Convert 150° to radians.
π radians = 180°, so 1° = π/180 radians
150° = 150 × π/180 = 5π/6 radians
Trigonometric Functions — Class 11
Trigonometry grows up in Class 11 — radians, all four quadrants and the addition formulas. Start with the ratios you can compute live.
Radian measureA full circle = 2π radians = 360°. Convert with π radians = 180°.
Sign in quadrantsUse "All-Silver-Tea-Cups": all positive in Q1, sin in Q2, tan in Q3, cos in Q4.
Fundamental identitiessin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ.
Compound anglessin(A±B) = sinA cosB ± cosA sinB; cos(A±B) = cosA cosB ∓ sinA sinB.
Trig ratio table & calculator Interactive
See the standard-angle table, then type any angle (in degrees) to get sin, cos and tan.
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | ½ | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | ½ | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
sin—
cos—
tan—
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Radian–degree | π radians = 180° |
| Pythagorean identity | sin²θ + cos²θ = 1 |
| sin(A+B) | sinA cosB + cosA sinB |
| cos(A+B) | cosA cosB − sinA sinB |
Common mistakes & exam wins
- Convert degrees to radians with × π/180, and radians to degrees with × 180/π.
- Use "All-Silver-Tea-Cups" to get the sign of a ratio in each quadrant.
- sin(90° − θ) = cos θ, and the co-ratios follow the same pattern.
Frequently asked questions
How do you convert degrees to radians?
Multiply the degree measure by π/180. For example, 180° = π radians.
What is the fundamental trigonometric identity?
sin²θ + cos²θ = 1.
What is the formula for sin(A + B)?
sin(A + B) = sinA cosB + cosA sinB.