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Questions and Answers
What is the definition of the sine function in a right-angled triangle?
What is the definition of the sine function in a right-angled triangle?
- adjacent side / hypotenuse
- opposite side / hypotenuse (correct)
- opposite side / adjacent side
- hypotenuse / opposite side
What is the period of the tangent function?
What is the period of the tangent function?
- π (correct)
- 3Ï€
- 2Ï€
- 4Ï€
Which identity relates the squares of the sine and cosine functions?
Which identity relates the squares of the sine and cosine functions?
- sin(A) + cos(A) = 1
- sin^2(A) + cos^2(A) = 1 (correct)
- sin(A)cos(A) = 1
- tan(A) = 1
What is an application of trigonometry in real-world problems?
What is an application of trigonometry in real-world problems?
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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 the definition of an angle in trigonometry?
What is the definition of an angle in trigonometry?
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Study Notes
Trigonometry
Definitions
- Angle: a measure of rotation between two lines or planes
- Trigonometric functions: functions that relate the ratios of the sides of a right-angled triangle
- Hypotenuse: the side opposite the right angle (90°) in a right-angled triangle
Trigonometric Functions
- 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
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 of Trigonometric Functions
- Sine and Cosine: periodic functions with period 2Ï€
- Tangent: periodic function with period π
Applications of Trigonometry
- Right Triangle Problems: solving for unknown sides or angles
- Wave Motion: modeling periodic phenomena, such as sound waves or light waves
- Navigation: calculating distances and directions using triangulation
Trigonometry
Definitions
- An angle is a measure of rotation between two lines or planes
- Trigonometric functions relate the ratios of the sides of a right-angled triangle
- The hypotenuse is the side opposite the right angle (90°) in a right-angled triangle
Trigonometric Functions
- Sine (sin) is the ratio of the opposite side to the hypotenuse
- Cosine (cos) is the ratio of the adjacent side to the hypotenuse
- Tangent (tan) is the ratio of the opposite side to the adjacent side
- Cotangent (cot) is the ratio of the adjacent side to the opposite side
- Secant (sec) is the ratio of the hypotenuse to the adjacent side
- Cosecant (csc) is the ratio of the hypotenuse to the opposite side
Identities
- The Pythagorean Identity states that sin^2(A) + cos^2(A) = 1
- The Sum and Difference Formulas for sine and cosine are:
- sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
- cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
Graphs of Trigonometric Functions
- Sine and cosine are periodic functions with a period of 2Ï€
- Tangent is a periodic function with a period of π
Applications of Trigonometry
- Right triangle problems involve solving for unknown sides or angles
- Trigonometry models periodic phenomena, such as sound waves or light waves, in wave motion
- Trigonometry is used in navigation to calculate distances and directions using triangulation
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