Question
What are the trigonometric ratios?
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Answer
Explain sine, cosine, and tangent rule?
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GPT 3.5
The trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent. These ratios are used in trigonometry to relate the angles of a triangle to the lengths of its sides.
Answered by
GPT 3.5
In trigonometry, the sine, cosine, and tangent rules are used to relate the angles of a right triangle to the lengths of its sides.
1. Sine rule: The sine rule states that the ratio of the length of the side opposite an angle to the length of the hypotenuse is equal to the sine of that angle. In other words, for a right triangle with angles A, B, and C (where C is the right angle) and sides a, b, and c (opposite angles A, B, and C, respectively), the sine rule can be written as:
sin(A) = a/c
sin(B) = b/c
2. Cosine rule: The cosine rule states that the ratio of the length of the side adjacent to an angle to the length of the hypotenuse is equal to the cosine of that angle. In other words, for a right triangle with angles A, B, and C (where C is the right angle) and sides a, b, and c (opposite angles A, B, and C, respectively), the cosine rule can be written as:
cos(A) = b/c
cos(B) = a/c
3. Tangent rule: The tangent rule states that the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle is equal to the tangent of that angle. In other words, for a right triangle with angles A, B, and C (where C is the right angle) and sides a, b, and c (opposite angles A, B, and C, respectively), the tangent rule can be written as:
tan(A) = a/b
tan(B) = b/a
These rules are essential for solving trigonometric problems involving right triangles.
1. Sine rule: The sine rule states that the ratio of the length of the side opposite an angle to the length of the hypotenuse is equal to the sine of that angle. In other words, for a right triangle with angles A, B, and C (where C is the right angle) and sides a, b, and c (opposite angles A, B, and C, respectively), the sine rule can be written as:
sin(A) = a/c
sin(B) = b/c
2. Cosine rule: The cosine rule states that the ratio of the length of the side adjacent to an angle to the length of the hypotenuse is equal to the cosine of that angle. In other words, for a right triangle with angles A, B, and C (where C is the right angle) and sides a, b, and c (opposite angles A, B, and C, respectively), the cosine rule can be written as:
cos(A) = b/c
cos(B) = a/c
3. Tangent rule: The tangent rule states that the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle is equal to the tangent of that angle. In other words, for a right triangle with angles A, B, and C (where C is the right angle) and sides a, b, and c (opposite angles A, B, and C, respectively), the tangent rule can be written as:
tan(A) = a/b
tan(B) = b/a
These rules are essential for solving trigonometric problems involving right triangles.
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