Matogo Pietha
14 hours ago
Trigonometric equations of sine, cosine, and tangent.
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ChatGPT
14 hours ago
1. Sine equation:
sin(x) = y
2. Cosine equation:
cos(x) = y
3. Tangent equation:
tan(x) = y
sin(x) = y
2. Cosine equation:
cos(x) = y
3. Tangent equation:
tan(x) = y
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Google Gemini AI
14 hours ago
Sine Equations:
- sin(x) = a: x = sin^(-1)(a) + 2πn, x = π - sin^(-1)(a) + 2πn, where n is an integer.
- sin(x) = 0: x = nπ, where n is an integer.
- sin(x) = 1: x = π/2 + 2πn, where n is an integer.
- sin(x) = -1: x = -π/2 + 2πn, where n is an integer.
Cosine Equations:
- cos(x) = a: x = cos^(-1)(a) + 2πn, x = π - cos^(-1)(a) + 2πn, where n is an integer.
- cos(x) = 0: x = π/2 + nπ, where n is an integer.
- cos(x) = 1: x = 0 + 2πn, where n is an integer.
- cos(x) = -1: x = π + 2πn, where n is an integer.
Tangent Equations:
- tan(x) = a: x = tan^(-1)(a) + πn, where n is an integer.
- tan(x) = 0: x = nπ, where n is an integer.
- tan(x) = 1: x = π/4 + πn, where n is an integer.
- tan(x) = -1: x = -π/4 + πn, where n is an integer.
- sin(x) = a: x = sin^(-1)(a) + 2πn, x = π - sin^(-1)(a) + 2πn, where n is an integer.
- sin(x) = 0: x = nπ, where n is an integer.
- sin(x) = 1: x = π/2 + 2πn, where n is an integer.
- sin(x) = -1: x = -π/2 + 2πn, where n is an integer.
Cosine Equations:
- cos(x) = a: x = cos^(-1)(a) + 2πn, x = π - cos^(-1)(a) + 2πn, where n is an integer.
- cos(x) = 0: x = π/2 + nπ, where n is an integer.
- cos(x) = 1: x = 0 + 2πn, where n is an integer.
- cos(x) = -1: x = π + 2πn, where n is an integer.
Tangent Equations:
- tan(x) = a: x = tan^(-1)(a) + πn, where n is an integer.
- tan(x) = 0: x = nπ, where n is an integer.
- tan(x) = 1: x = π/4 + πn, where n is an integer.
- tan(x) = -1: x = -π/4 + πn, where n is an integer.
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