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Questions and Answers
What is the definition of trigonometry?
What is the definition of trigonometry?
What is the mnemonic used to remember the trig ratios?
What is the mnemonic used to remember the trig ratios?
What is the Pythagorean Identity?
What is the Pythagorean Identity?
What is the name of the formula used to find the sine of a double angle?
What is the name of the formula used to find the sine of a double angle?
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What is the formula for sin(A + B)?
What is the formula for sin(A + B)?
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What is an application of trigonometry in real-life scenarios?
What is an application of trigonometry in real-life scenarios?
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Study Notes
Trigonometry
Definitions
- Trigonometry: Study of relationships between the sides and angles of triangles, especially triangles with right angles (90 degrees)
- Angles: Measured in degrees, radians, or gradians
- Triangles: Classified as right-angled, oblique, or oblique-angled
Key Concepts
-
SOH-CAH-TOA: Mnemonic to remember trig ratios:
- Sine (sin) = Opposite side / Hypotenuse
- Cosine (cos) = Adjacent side / Hypotenuse
- Tangent (tan) = Opposite side / Adjacent side
- Pythagorean Identity: sin^2(A) + cos^2(A) = 1
-
Trigonometric Ratios:
- sine (sin)
- cosine (cos)
- tangent (tan)
- cotangent (cot)
- secant (sec)
- cosecant (csc)
Identities and Formulas
-
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)
-
Double Angle Formulas:
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos^2(A) - sin^2(A)
-
Half Angle Formulas:
- sin(A/2) = ±√((1 - cos(A))/2)
- cos(A/2) = ±√((1 + cos(A))/2)
Applications
- Right Triangle Problems: Solve for sides and angles using trig ratios
- Wave Motion: Model periodic motion using trig functions (e.g., sound, light)
- Analytic Geometry: Use trig to solve problems involving circles, ellipses, and triangles in coordinate systems
Trigonometry
Basic Concepts
- Trigonometry is the study of relationships between sides and angles of triangles, especially right-angled triangles
- Angles can be measured in degrees, radians, or gradians
- Triangles can be classified as right-angled, oblique, or oblique-angled
Trigonometric Ratios
- Sine (sin): Opposite side / Hypotenuse
- Cosine (cos): Adjacent side / Hypotenuse
- Tangent (tan): Opposite side / Adjacent side
- Cotangent (cot): Adjacent side / Opposite side
- Secant (sec): Hypotenuse / Adjacent side
- Cosecant (csc): Hypotenuse / Opposite side
Pythagorean Identity and Identities
- 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)
-
Double Angle Formulas:
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos^2(A) - sin^2(A)
-
Half Angle Formulas:
- sin(A/2) = ±√((1 - cos(A))/2)
- cos(A/2) = ±√((1 + cos(A))/2)
Applications of Trigonometry
- Right Triangle Problems: Solve for sides and angles using trig ratios
- Wave Motion: Model periodic motion using trig functions (e.g., sound, light)
- Analytic Geometry: Use trig to solve problems involving circles, ellipses, and triangles in coordinate systems
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Description
Learn the fundamental concepts of trigonometry, including definitions of angles, triangles, and trig ratios. Understand the SOH-CAH-TOA mnemonic to remember sine, cosine, and tangent.
