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Questions and Answers
Wanem olgeta samting we oli stap long eniwan long olgeta pikininiia taem oli bon?
Wanem olgeta samting we oli stap long eniwan long olgeta pikininiia taem oli bon?
Wanem oli stap long eniwan long olgeta pikininiia taem oli bon?
Wanem oli stap long eniwan long olgeta pikininiia taem oli bon?
What is the relationship between the sine and cosine functions at an angle of 90 degrees?
What is the relationship between the sine and cosine functions at an angle of 90 degrees?
If the sine of an angle is negative, what can you conclude about the angle?
If the sine of an angle is negative, what can you conclude about the angle?
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What is the period of the trigonometric function $y = 2sin(x)$?
What is the period of the trigonometric function $y = 2sin(x)$?
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If the cosine of an angle is 0.5, what is the sine of the angle?
If the cosine of an angle is 0.5, what is the sine of the angle?
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Which of the following statements accurately describes the relationship between the unit circle and trigonometric functions?
Which of the following statements accurately describes the relationship between the unit circle and trigonometric functions?
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Flashcards
Concept 1
Concept 1
One of the key ideas or principles underlying the content.
Concept 2
Concept 2
Another important theme that supports the main idea.
Concept 3
Concept 3
A distinct characteristic that defines part of the content.
Concept 4
Concept 4
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Concept 5
Concept 5
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Unit Circle
Unit Circle
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Sine Function
Sine Function
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Cosine Function
Cosine Function
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Range of Sine Function
Range of Sine Function
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Range of Cosine Function
Range of Cosine Function
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Study Notes
Angle Measurement
- An angle is formed by rotating a ray (half-line) around its endpoint.
- The starting position is the initial side, and the final position is the terminal side.
- The endpoint is the vertex.
- Angles can be positive (counterclockwise) or negative (clockwise).
- Angles are often labeled with Greek letters (e.g., α, β, θ) or uppercase letters (e.g., A, B, C).
- Coterminal angles have the same initial and terminal sides. These angles can be found by adding or subtracting multiples of 2π.
Radian Measure
- One radian (rad) is the measure of a central angle that intercepts an arc equal in length to the radius of the circle.
- An angle is measured in radians by the formula: θ = s/r, where s is the arc length and r is the radius.
- If the radius is 1, the radian measure equals the arc length.
- Radians are a unit of angle measure that can be used to express the measure of a central angle in a circle. Radians are useful in calculus.
Degree Measure
- A degree (°) is a unit of angle measure.
- One degree is 1/360 of a complete revolution around a point.
- Fractional parts of degrees are measured in minutes (') and seconds ("). (i.e. 1 minute = (1/60) degree and 1 second = (1/3600) degree)
- Degrees are commonly used for everyday measurements.
Conversions Between Degrees and Radians
- To convert degrees to radians, multiply by π/180°.
- To convert radians to degrees, multiply by 180°/π.
Complementary and Supplementary Angles
- Complementary angles add up to 90° (or π/2 radians).
- Supplementary angles add up to 180° (or π radians).
Finding Arc Length
- The arc length (s) of a circle is given by the formula s = rθ, where r is the radius and θ is the angle in radians.
- The arc length is the portion of the circumference of a circle that is intercepted by a central angle.
Linear and Angular Speed
- Linear speed is the distance traveled per unit time along a circular path. It is calculated as s/t (arc length/time).
- Angular speed is the rate at which an angle is changing per unit time ( θ/t).
- Linear speed is measured in units of length per unit of time (e.g., cm/s, m/s).
- Angular speed is measured in units of radians per unit of time (e.g., rad/s).
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Description
Quiz ia blong helpem yu long tingting long angle measurement mo radian degrees. Yu go long olgeta samting olsem angle, vertex, mo olsem wanem blong calculate angles long degrees mo radians. Lingkol blong angle mo formule blong measure i stap tu.
