Properties of trigonometric functions
Read the properties of sine, cosine and cotangent from their graphs: period, parity, zeros, intervals of decrease, domain and range.
- أوكرانيا: الصف ١٠
- روسيا: الصف ١٠
- ألمانيا: الصف ١٠
- فرنسا: الصف ١١
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الدليل
For Ukrainian Grade 10 (algebra and analysis, section 2, item 11). For each function the book lists the domain D, the range E, the period, parity, zeros, intervals of constant sign and of monotonicity, and the extremes. The graphs are called the sinusoid, cosinusoid, tangentoid and cotangentoid. Angles are in radians. The x-axis shows plain numbers: π ≈ ٣٫١٤, 2π ≈ ٦٫٢٨.
The smallest positive period is the main period: ٢π for sin and cos, π for tg and ctg. Sine, tangent and cotangent are odd; cosine is even. The function y = ctg x is defined for x ≠ πn and its graph is separate branches; ctg has zeros at π٢ + πn.
Common slips: period 2π for cotangent; thinking sine is even; looking for decreasing intervals between zeros; counting the breaks of cotangent as zeros.