Radians
Measure angles using the circle, then connect them to trigonometry and geometry.
Choose an available lesson below. More radian lessons are being added.
- Radians and degreesUnderstand one radian, convert degrees and radians exactly, and interpret signed angles and full turns. Move the circle yourself, then practise with worked solutions.
- Exact trigonometric values in radiansFind exact sine, cosine and tangent values in radians using special triangles and the unit circle. Practise reference angles, quadrant signs and extra turns with worked solutions.
- Trigonometric graphs in radiansSketch sine, cosine and tangent graphs in radians. Find periods, ranges, shifts, exact intercepts and asymptotes with a manual graph explorer and worked practice.
- Arc length and sector perimeterUse l = rθ to find arc lengths and sector perimeters. Work with major arcs, chords, annular sectors and curved boundaries using a manual model and original worked questions.
- Area of a sectorFind sector and annular-sector areas in radians. Recover missing dimensions, combine area with perimeter, compare equal areas and handle measurement bounds with worked practice.
- Area of a segmentFind minor and major segment areas using sectors and triangles. Recover angles from chords or sagitta, form area-ratio equations and solve curved cross-section problems.
- Radians in circle geometry problemsSolve radian geometry problems involving tangents, inscribed circles and overlapping circles. Build consistent diagrams and separate curved areas from their boundaries.
- Trigonometric equations in radiansSolve sine, cosine and tangent equations in radians. Find every solution in positive or negative intervals, handle endpoints and check the sine-rule ambiguous case.
- Multiple and shifted angle equationsSolve trigonometric equations containing 2x, 3x or shifted angles. Transform the whole interval, map every root back and preserve denominator restrictions.