Trigonometer Integrating Rotating Radius for Direct Trigonometric Readings
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Solution Overview
Problem
Students and carpenters face difficulties in understanding and applying trigonometric concepts due to the complexity of drawing trigonometric circles and the need for multiple measurement tools, which hinders effective learning and practical applications in carpentry.
Innovation Solution
The New Trigonometer, a measurement tool that integrates an Angle Tracking Device, Tangent Calculator, and Sin/Cos Calculator with a conventional protractor, allowing for geometric visualization of trigonometric functions, reducing the need for drawing and minimizing the number of tools required.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If students use traditional methods to draw trigonometric circles with multiple tools (paper, ruler, pencil, set square, compass, protractor), then they can obtain trigonometric function values, but the process consumes excessive time and complicates the learning procedure
Solution Approach 1:
The patent combines the protractor with a rotating radius mechanism and trigonometric function scales directly on the device body. This integration allows students to obtain sine, cosine, and tangent values by simply rotating the radius to the desired angle and reading the values directly from the scales, eliminating the need to draw the entire trigonometric circle with multiple tools.
Solution Approach 2:
The device serves multiple functions: it acts as a protractor for angle measurement, a trigonometric circle for visualizing relationships, and a direct reading instrument for obtaining sine, cosine, and tangent values. This multi-functionality consolidates what previously required separate tools and procedures into a single instrument.
2Loss of information
If students rely on drawing trigonometric circles on paper, then they can visualize trigonometric relationships, but it is very difficult to imagine and understand the rotating radius concept
Solution Approach 1:
The patent introduces a rotating radius mechanism that can physically move to different angles. This dynamic element allows students to see the radius actually rotate and change position, making the abstract concept of a rotating radius concrete and intuitive. The rotation is centered on the protractor's center point, naturally demonstrating the trigonometric circle geometry.
3Measurement precision
If carpenters use traditional measurement tools (layout square, steel square) to determine angles and slopes, then they can perform measurements, but they still need to perform calculations based on rafter tables
Solution Approach 1:
The device serves multiple functions: it acts as a protractor for angle measurement, a trigonometric circle for visualizing relationships, and a direct reading instrument for obtaining sine, cosine, and tangent values. This multi-functionality consolidates what previously required separate tools and procedures into a single instrument.
4Ease of operation
If carpenters use multiple measurement tools (layout square, steel square), then they can determine various measurements, but the complexity of the carpentry process increases
Solution Approach 1:
The patent combines the protractor with a rotating radius mechanism and trigonometric function scales directly on the device body. This integration allows students to obtain sine, cosine, and tangent values by simply rotating the radius to the desired angle and reading the values directly from the scales, eliminating the need to draw the entire trigonometric circle with multiple tools.
Data Source
AI summary
The New Trigonometer is a device used to compute the trigonometric sine, cosine and tangent of angles. Consequently, the device could also be used to calculate the reciprocal sine, cosine, and tangent functions. The device constitutes of a protractor and a graduated ruler attached thereof. An arm is pivotally joined to the center of protractor and a second graduated ruler is pivotally joined to the arm in a way, which makes the New Trigonometer a reflection of the trigonometric circle.