Proof Without Words: A Trigonometric Identity for sec x + tan x

2015 ◽  
Vol 88 (2) ◽  
pp. 151-151 ◽  
Author(s):  
Roger B. Nelsen
Keyword(s):  
Trigonometric Identity

A Remarkable Trigonometric Identity

1977 ◽  
Vol 70 (5) ◽  
pp. 452-455
Author(s):  
Eli Maor
Keyword(s):  
Physical Interpretation ◽  
Trigonometric Identity

An unusual trigonometric identity and its physical interpretation.

Technology and Reasoning in Algebra and Geometry

1996 ◽  
Vol 89 (2) ◽  
pp. 138-142
Author(s):  
Daniel B. Hirschhorn ◽  
Denisse R. Thompson
Keyword(s):  
Number Theory ◽  
Mathematical Induction ◽  
Educational Progress ◽  
National Assessment ◽  
Trigonometric Identity ◽  
Reasoning Skills ◽  
Geometry Teachers ◽  
Long Course

If one topic is likely to be stressed by algebra and geometry teachers, it is reasoning. In algebra classes, students are constantly being asked to show their work and justify their simplifications, often without formal connection to proof concepts or the proof process. In geometry classes, students are expected to learn how to write simple proofs. However, evidence shows that students are not learning these reasoning skills. In the 1985–86 National Assessment of Educational Progress, Silver and Carpenter (1989, 18) found that “many eleventhgrade students are confused about the fundamental distinctions among mathematical demonstrations, assumptions, and proofs.” Most students thought a theorem was a demonstration or an assumption. Senk (1985) found that only about 30 percent of students mastered proof wTiting in geometry, despite being enrolled in a year-long course emphasizing proof. Thompson (1992) found that roughly 60 percent of precalculus students were successful at trigonometric-identity proofs, more than 30 percent could complete number-theory proofs dealing with divisibility, and less than 20 percent could handle indirect arguments or proof by mathematical induction.

scholarly journals Student’s Difficulty Identification in Completing the Problem of Equation and Trigonometry Identities

2019 ◽  
Vol 2 (1) ◽  
pp. 34 ◽  
Author(s):  
Siti Maryam Rohimah ◽  
Sufyani Prabawanto
Keyword(s):  
High School Students ◽  
School Students ◽  
Quadratic Equations ◽  
Trigonometric Identity ◽  
Ability Tests ◽  
Solving Equations ◽  
Data Collection Technique ◽  
Trigonometric Equations ◽  
Identity Problems ◽  
Trigonometric Identities

This study aims to identify the types of difficulties experienced by high school students in solving equations and trigonometric identities. The method used in this research is descriptive qualitative research method because researchers want to describe or describe the facts of students' difficulties in solving equations and trigonometric identities. The data collection technique in this study is by using respondents' ability tests and interviews. Based on the results of data analysis, there are three aspects of students 'difficulties in solving trigonometric equations and also there are three aspects of students' difficulties in solving trigonometric identity problems. The difficulties of students in solving trigonometric equations, namely the difficulty of students in deciphering the form of the problem, difficulty in factoring in the form of trigonometric quadratic equations, and difficulties using the basic trigonometric equations. Whereas, the difficulties of students in solving trigonometric identity problems, namely the difficulty of students applying general trigonometry formulas, difficulty describing each of the trigonometric comparison relationships, and difficulties in performing algebraic calculations/computation.

Symbolically Automated Direct Kinematic Equations Solver for Robotic Manipulators

Robotica ◽  
1989 ◽  
Vol 7 (3) ◽  
pp. 243-254 ◽  
Author(s):  
C.Y. Ho ◽  
Jen Sriwattanathamma
Keyword(s):  
Jacobian Matrix ◽  
Robotic Manipulators ◽  
Industrial Robots ◽  
Heuristic Rules ◽  
Symbolic Form ◽  
Rule Based ◽  
Transformation Matrices ◽  
Trigonometric Identity ◽  
System A ◽  
Forward Kinematic

SUMMARYSolving the direct kinematic problem in a symbolic form requires a laborious process of successive multiplications of the link homogeneous transformation matrices and involves a series of algebraic and trigonometric simplifications. The manual production of such solutions is tedious and error-prone. Due to the efficiency of the Prolog language in symbolic processing, a rule–based Prolog program is developed to automate the creation of the following processes: Link transformation matrices; forward kinematic solutions; and the Jacobian matrix. This paper presents the backward recursive formulation techniques, the trigonometric identity rules, and some heuristic rules for implementing the System. A verification of the System has been demonstrated in case of several industrial robots.

Sharing Teaching Ideas: Discovering New Trigonometric Identities

2003 ◽  
Vol 96 (9) ◽  
pp. 650-653
Author(s):  
Sheldon P. Gordon
Keyword(s):  
Trigonometric Identity ◽  
Teaching Ideas ◽  
Rare Opportunity ◽  
As If ◽  
Trigonometric Identities

For most of our students, trigonometric identities appear as if by magic. A recent class activity gave me the rare opportunity to lead my students to discover what appears to be a new trigonometric identity by using a combination of graphical, numerical, and algebraic tools. In this article, I demonstrate this result and then show how it can be extended to a wider class of apparently new identities that are all extensions of the Pythagorean identity.

Proof for a q-Trigonometric Identity of Gosper

2020 ◽  
Vol 17 (5) ◽  
Author(s):  
Bing He ◽  
Fuli He ◽  
Hongcun Zhai
Keyword(s):  
Trigonometric Identity
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