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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?
What is the period of the tangent function?
What is the period of the tangent function?
Which identity relates the squares of the sine and cosine functions?
Which identity relates the squares of the sine and cosine functions?
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 2π
- 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 2π
- 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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Description
Test your understanding of basic trigonometric concepts, including angles, trigonometric functions, and key ratios. Review definitions of sine, cosine, and tangent, and apply them to solve problems.
