Trigonometric identities and proof
Use sin٢θ + cos٢θ = ١ and tanθ = sinθcosθ to find one ratio from another, spot the faulty line in a ‘proof’, and learn what counts as a proof of an مطابقة.
- سوريا: الصف ٩
- فلسطين: الصف ٩
- إيران: الصف ١٠
- أفغانستان: الصف ١١
- أوكرانيا: الصف ٨
- روسيا: الصف ١٠
- ألمانيا: الصف ١٠
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
For Afghan Grade 11 (chapter 2: trigonometric identities), Iran Grade 10–11 and A-level. In the picture a circle of radius 3 squares stands for radius 1, and P is at (cosθ,sinθ) = (٠٫٦,٠٫٨): the 3-4-5 triangle.
An مطابقة is true for every angle for which both sides are defined. The basic ones are sin٢θ + cos٢θ = ١ (Pythagoras in the triangle with hypotenuse 1) and tanθ = sinθcosθ. Dividing the first by cos٢θ gives ١ + tan٢θ = ١cos٢θ.
To prove an identity, work on one side only (usually the more complicated one), with steps that are always true, until it becomes the other side. Checking one angle is not a proof, and neither is starting from the result you want.