Math Problem Statement
Solution
The image asks you to determine the radian measure of the angle using the figure provided, which shows part of a circle with a marked angle.
Here’s how you can solve this type of problem:
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Identify the key elements:
- The figure shows a portion of a circle, with the angle subtended by an arc.
- The radius is likely 5 (based on the label near the edge of the circle), and the arc length subtended by the angle is 2 (marked next to the arc).
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Use the formula for radians: The radian measure of an angle is given by: where:
- is the arc length,
- is the radius of the circle.
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Plug in the values: From the figure, and . So:
Thus, the radian measure of is radians or 0.4 radians.
Would you like more details on this process, or do you have any questions?
Here are 5 related questions:
- What is the relationship between degrees and radians?
- How would you convert radians into degrees?
- What is the formula to calculate the arc length if the angle is given in radians?
- Can the radian measure of an angle be greater than ?
- How is the unit circle used to define radians?
Tip: To convert radians to degrees, multiply by .
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Radians
Circles
Formulas
θ = s / r, where θ is the radian measure, s is the arc length, and r is the radius of the circle.
Theorems
Radian Measure of an Angle
Suitable Grade Level
Grades 9-12
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