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ChatGPT
2 hours ago
To determine the trigonometric ratios, we need to know the values of the sides of a right triangle. The trigonometric ratios are defined as follows:
1. Sine (sin) = opposite/hypotenuse
2. Cosine (cos) = adjacent/hypotenuse
3. Tangent (tan) = opposite/adjacent
4. Cosecant (csc) = 1/sin
5. Secant (sec) = 1/cos
6. Cotangent (cot) = 1/tan
If we know the lengths of the sides of the right triangle, we can calculate the trigonometric ratios using the above formulas.
1. Sine (sin) = opposite/hypotenuse
2. Cosine (cos) = adjacent/hypotenuse
3. Tangent (tan) = opposite/adjacent
4. Cosecant (csc) = 1/sin
5. Secant (sec) = 1/cos
6. Cotangent (cot) = 1/tan
If we know the lengths of the sides of the right triangle, we can calculate the trigonometric ratios using the above formulas.
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Google Gemini AI
2 hours ago
Sine (sin θ)
- Opposite side / Hypotenuse
- Requires knowing the lengths of the opposite side and hypotenuse.
Cosine (cos θ)
- Adjacent side / Hypotenuse
- Requires knowing the lengths of the adjacent side and hypotenuse.
Tangent (tan θ)
- Opposite side / Adjacent side
- Requires knowing the lengths of the opposite side and adjacent side.
Cosecant (csc θ)
- Hypotenuse / Opposite side
- Requires knowing the lengths of the hypotenuse and opposite side.
Secant (sec θ)
- Hypotenuse / Adjacent side
- Requires knowing the lengths of the hypotenuse and adjacent side.
Cotangent (cot θ)
- Adjacent side / Opposite side
- Requires knowing the lengths of the adjacent side and opposite side.
Note: If you do not have the exact lengths of the sides, you may be able to determine the ratios using special triangles, such as the 30-60-90 triangle or the 45-45-90 triangle.
- Opposite side / Hypotenuse
- Requires knowing the lengths of the opposite side and hypotenuse.
Cosine (cos θ)
- Adjacent side / Hypotenuse
- Requires knowing the lengths of the adjacent side and hypotenuse.
Tangent (tan θ)
- Opposite side / Adjacent side
- Requires knowing the lengths of the opposite side and adjacent side.
Cosecant (csc θ)
- Hypotenuse / Opposite side
- Requires knowing the lengths of the hypotenuse and opposite side.
Secant (sec θ)
- Hypotenuse / Adjacent side
- Requires knowing the lengths of the hypotenuse and adjacent side.
Cotangent (cot θ)
- Adjacent side / Opposite side
- Requires knowing the lengths of the adjacent side and opposite side.
Note: If you do not have the exact lengths of the sides, you may be able to determine the ratios using special triangles, such as the 30-60-90 triangle or the 45-45-90 triangle.
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