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Questions and Answers
Which of the following is a Pythagorean identity?
Which of the following is a Pythagorean identity?
- tan(x) = sin(x)/cos(x)
- 1 + tan²(x) = sec²(x) (correct)
- sin(x) = 1/csc(x)
- cot(x) = cos(x)/sin(x)
The area of a triangle can be calculated using the formula Area = (1/2)ab * cos(C).
The area of a triangle can be calculated using the formula Area = (1/2)ab * cos(C).
False (B)
What is the double angle formula for sine?
What is the double angle formula for sine?
sin(2x) = 2sin(x)cos(x)
The law of sines states that a/sin(A) = b/sin(B) = c/sin(C). Fill in the blank. The ratio of side 'b' over sin(B) is equal to _____ over sin(A).
The law of sines states that a/sin(A) = b/sin(B) = c/sin(C). Fill in the blank. The ratio of side 'b' over sin(B) is equal to _____ over sin(A).
Match the trigonometric identities with their corresponding formulas:
Match the trigonometric identities with their corresponding formulas:
Flashcards
Reciprocal Identities
Reciprocal Identities
Relates the sine, cosine, and tangent of an angle to the cosecant, secant, and cotangent of the same angle.
Pythagorean Identities
Pythagorean Identities
States that the square of the sine of an angle plus the square of the cosine of the same angle equals 1.
Law of Cosines
Law of Cosines
Used to solve triangles where you know two sides and the included angle or two angles and one side.
Law of Sines
Law of Sines
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Sum and Difference Formulas
Sum and Difference Formulas
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Study Notes
Trigonometric Identities
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Reciprocal Identities: These relate trigonometric functions to each other.
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sin(x) = 1/csc(x), cos(x) = 1/sec(x), tan(x) = 1/cot(x)
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csc(x) = 1/sin(x), sec(x) = 1/cos(x), cot(x) = 1/tan(x)
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Pythagorean Identities: Based on the Pythagorean theorem, these connect sine and cosine.
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sin²(x) + cos²(x) = 1
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1 + tan²(x) = sec²(x)
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1 + cot²(x) = csc²(x)
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Quotient Identities: These define tangent and cotangent in terms of sine and cosine.
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tan(x) = sin(x)/cos(x)
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cot(x) = cos(x)/sin(x)
Law of Cosines & Law of Sines
- Law of Cosines: Used to find sides and angles in triangles.
- c² = a² + b² - 2ab * cos(C)
- Law of Sines: Another useful tool for finding unknown sides and angles.
- a/sin(A) = b/sin(B) = c/sin(C)
Area of a Triangle (Trigonometric Form)
- Calculating the area of a triangle using trigonometric functions.
- Area = (1/2)ab * sin(C)
Sum and Difference Formulas
- Sine:
- sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
- Cosine:
- cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
- Tangent:
- tan(A ± B) = [tan(A) ± tan(B)] / [1 ∓ tan(A)tan(B)]
Double Angle Formulas
- Sine:
- sin(2x) = 2sin(x)cos(x)
- Cosine:
- cos(2x) = cos²(x) - sin²(x) = 2cos²(x) - 1 = 1 - 2sin²(x)
- Tangent:
- tan(2x) = 2tan(x) / [1 - tan²(x)]
Half-Angle Formulas
- Sine:
- sin(x/2) = ±√[(1 - cos(x))/2]
- Cosine:
- cos(x/2) = ±√[(1 + cos(x))/2]
- Tangent:
- tan(x/2) = ±√[(1 - cos(x))/(1 + cos(x))]
- tan(x/2) = sin(x) / [1 + cos(x)] or [1 - cos(x)] / sin(x)
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