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Questions and Answers
What is the value of sin^2(A) + cos^2(A) in a right-angled triangle?
What is the ratio of the opposite side to the hypotenuse in a right-angled triangle?
What is the formula for sin(A + B) in a right-angled triangle?
What is the formula for cos(2A) in a right-angled triangle?
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What is the formula for tan(A + B) in a right-angled triangle?
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What is the formula for sin(A/2) in a right-angled triangle?
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What is the ratio of the adjacent side to the opposite side in a right-angled triangle?
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What is the ratio of the hypotenuse to the opposite side in a right-angled triangle?
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Study Notes
Trigonometric Ratios
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Sine (sin): The ratio of the opposite side to the hypotenuse in a right-angled triangle.
- sin(A) = opposite side / hypotenuse
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Cosine (cos): The ratio of the adjacent side to the hypotenuse in a right-angled triangle.
- cos(A) = adjacent side / hypotenuse
-
Tangent (tan): The ratio of the opposite side to the adjacent side in a right-angled triangle.
- tan(A) = opposite side / adjacent side
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Cotangent (cot): The ratio of the adjacent side to the opposite side in a right-angled triangle.
- cot(A) = adjacent side / opposite side
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Secant (sec): The ratio of the hypotenuse to the adjacent side in a right-angled triangle.
- sec(A) = hypotenuse / adjacent side
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Cosecant (csc): The ratio of the hypotenuse to the opposite side in a right-angled triangle.
- csc(A) = hypotenuse / opposite side
Trigonometric Identities
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Pythagorean Identity:
- sin^2(A) + cos^2(A) = 1
-
Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
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Double Angle Formulas:
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos^2(A) - sin^2(A)
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Half Angle Formulas:
- sin(A/2) = ±√((1 - cos(A)) / 2)
- cos(A/2) = ±√((1 + cos(A)) / 2)
Trigonometric Ratios
- Sine (sin): Ratio of the opposite side to the hypotenuse in a right-angled triangle.
- Cosine (cos): Ratio of the adjacent side to the hypotenuse in a right-angled triangle.
- Tangent (tan): Ratio of the opposite side to the adjacent side in a right-angled triangle.
- Cotangent (cot): Ratio of the adjacent side to the opposite side in a right-angled triangle.
- Secant (sec): Ratio of the hypotenuse to the adjacent side in a right-angled triangle.
- Cosecant (csc): Ratio of the hypotenuse to the opposite side in a right-angled triangle.
Trigonometric Identities
- Pythagorean Identity: sin^2(A) + cos^2(A) = 1.
-
Sum and Difference Formulas: used to find trigonometric values of sums and differences of angles.
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
-
Double Angle Formulas: used to find trigonometric values of double angles.
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos^2(A) - sin^2(A)
-
Half Angle Formulas: used to find trigonometric values of half angles.
- sin(A/2) = ±√((1 - cos(A)) / 2)
- cos(A/2) = ±√((1 + cos(A)) / 2)
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Description
Learn about sine, cosine, tangent, and cotangent ratios in right-angled triangles, including their definitions and formulas.
