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Questions and Answers
What is the definition of the trigonometric ratio sine?
What is the definition of the trigonometric ratio sine?
What is the period of the cosine graph?
What is the period of the cosine graph?
What is the formula for the sum of sine and cosine of two angles?
What is the formula for the sum of sine and cosine of two angles?
What is the name of the identity that states sin^2(A) + cos^2(A) = 1?
What is the name of the identity that states sin^2(A) + cos^2(A) = 1?
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What is the application of trigonometry in modeling periodic motion?
What is the application of trigonometry in modeling periodic motion?
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What is the name of the trigonometric ratio that is the reciprocal of the sine?
What is the name of the trigonometric ratio that is the reciprocal of the sine?
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Study Notes
Trigonometry
Definition
- Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles.
Key Concepts
- Angles: Measured in degrees, radians, or gradians.
- Triangles: Right-angled, oblique, and oblique-angled triangles.
- Trigonometric Ratios: Sine, cosine, tangent, cotangent, secant, and cosecant.
Trigonometric Ratios
- Sine (sin): Opposite side over hypotenuse
- Cosine (cos): Adjacent side over hypotenuse
- Tangent (tan): Opposite side over adjacent side
- Cotangent (cot): Adjacent side over opposite side
- Secant (sec): Hypotenuse over adjacent side
- Cosecant (csc): Hypotenuse over opposite side
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)
Graphs
-
Sine and Cosine Graphs:
- Period: 2π
- Amplitude: 1
- Phase shift:Horizontal shift
-
Tangent Graph:
- Period: π
- Asymptotes: Vertical lines
Applications
- Right Triangle Problems: Finding sides and angles in right-angled triangles.
- Wave Motion: Modeling periodic motion, such as sound and light waves.
- Analytic Geometry: Solving problems involving triangles and circles.
Trigonometry
Definition
- Trigonometry deals with relationships between sides and angles of triangles.
Key Concepts
- Angles can be measured in degrees, radians, or gradians.
- Triangles can be right-angled, oblique, or oblique-angled.
- There are six trigonometric ratios: sine, cosine, tangent, cotangent, secant, and cosecant.
Trigonometric Ratios
- Sine (sin) is the ratio of opposite side to hypotenuse.
- Cosine (cos) is the ratio of adjacent side to hypotenuse.
- Tangent (tan) is the ratio of opposite side to adjacent side.
- Cotangent (cot) is the ratio of adjacent side to opposite side.
- Secant (sec) is the ratio of hypotenuse to adjacent side.
- Cosecant (csc) is the ratio of hypotenuse to opposite side.
Identities
- The Pythagorean Identity is sin^2(A) + cos^2(A) = 1.
- The Sum and Difference Formulas are:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Graphs
- Sine and cosine graphs have a period of 2π, amplitude of 1, and phase shift as a horizontal shift.
- Tangent graphs have a period of π and vertical asymptotes.
Applications
- Trigonometry is used to solve right triangle problems, involving finding sides and angles.
- Trigonometry models wave motion, such as sound and light waves, which involve periodic motion.
- Trigonometry is used in analytic geometry to solve problems involving triangles and circles.
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Description
Learn the fundamental concepts of trigonometry, including angles, triangles, and trigonometric ratios such as sine, cosine, and tangent.
