Related angles, arcs and sectors
Mirror a point on the unit circle to see how the sine and cosine of θ and 180° − θ are linked, use the reference angle to find cos 120°, then work out the length of an arc and the area of a sector with the angle in radians.
- سوريا: الصف ١٠
- فلسطين: الصف ١٠
- إيران: الصف ١١
- أفغانستان: الصف ١٠
- أوكرانيا: الصف ١٠
- روسيا: الصف ١٠
- ألمانيا: الصف ١٠
- فرنسا: الصف ١١
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
For Afghan Grade 10 (chapter 4: relations between the ratios of different angles; chapter 5: arc length and sector area), Iran Grade 11 and A-level. The coloured dots can be dragged; the readouts update live.
Point P is at angle θ on the الدائرة المثلثية. Its mirror image Q in the y-axis is at angle ١٨٠° − θ. They are at the same height, so sin (١٨٠° − θ) = sinθ, but their x-coordinates are opposite, so cos (١٨٠° − θ) = −cosθ. Reflecting in the x-axis, or turning through 180°, gives the other related angles in the same way.
An قوس of a circle of radius r that subtends an angle θ in radians has length l = rθ. The قطاع دائري it cuts off has area A = r٢θ٢.
The angle must be in radians: ٦٠° = π٣. Putting degrees into these formulas gives a wrong answer.