What are trigonometric formulas? When do students in Vietnam learn trigonometric formulas according to current regulations?

What are trigonometric formulas?

Trigonometric formulas are mathematical expressions that describe the relationships between the sides and angles in a right triangle. They are widely used in many different fields, from pure mathematics to physics, engineering, and even music.

*Note: Information is for reference only./.

What are trigonometric formulas? When do students in Vietnam learn trigonometric formulas according to current regulations? (Image from the Internet)

When do students in Vietnam learn trigonometric formulas?

Firstly, based on Section III of the Appendix in the General Education Program for Mathematics issued with Circular 32/2018/TT-BGDDT, the objectives for general secondary education include the following main goals:

- Contributing to the formation and development of mathematical competence with the required achievements: posing and answering questions during reasoning and problem-solving; using reasoning methods such as induction and deduction to understand various ways of solving problems; establishing mathematical models to describe situations, thereby proposing solutions to the presented mathematical problems in the established model; executing and presenting problem-solving solutions, evaluating the implemented solutions, reflecting on their value, and generalizing for similar problems; using tools and means for studying mathematics in learning, exploring, and solving mathematical problems.

- Possessing essential and basic mathematical knowledge and skills in:

+ Algebra and Some Aspects of Calculus: Calculating and using computational tools; using algebraic language and symbols; transforming algebraic and transcendental expressions (trigonometric, exponential, logarithmic), equations, systems of equations, inequalities; recognizing basic elementary functions (power, trigonometric, exponential, logarithmic); analyzing functions and drawing function graphs using derivative tools; using functional language and graphs to describe and analyze certain processes and phenomena in the real world; using integration to compute the area of flat shapes and the volume of objects in space.

Additionally, in Section V of the Appendix in the General Education Program for Mathematics issued with Circular 32/2018/TT-BGDDT, one of the contents of the grade 9 mathematics curriculum includes:

- Recognizing the sine (sin), cosine (cos), tangent (tan), and cotangent (cot) values of acute angles.

- Explaining the trigonometric ratios of special acute angles (30°, 45°, 60°) and complementary angles.

- Calculating the trigonometric ratios of acute angles accurately or approximately using a handheld calculator.

- Explaining some relations between the sides and angles in a right triangle (e.g., the opposite side equals the hypotenuse times the sine of the opposite angle or cosine of the adjacent angle; the opposite side equals the other opposite side times the tangent of the opposite angle or cotangent of the adjacent angle).

- Solving some practical problems related to trigonometric ratios of acute angles (e.g., calculating the length of a segment, the magnitude of an angle, and applying to solve right triangles, etc.).

In short, students learn trigonometric formulas in grade 9.

What is the teaching method for grade 9 mathematics in Vietnam?

Based on Section VI of the General Education Program for Mathematics issued with Circular 32/2018/TT-BGDDT, the teaching method for mathematics in general, and grade 9 mathematics in particular, will utilize the following methods:

- The teaching method in the Mathematics Curriculum meets the following basic requirements:

+ Suitable for students' cognitive processes (moving from concrete to abstract, from easy to difficult); not only emphasizing the logical nature of mathematical science but also considering the approach based on students' experience and their experiential learning;

+ Adhering to the concept of “learner-centered,” fostering positivity, autonomy, attention to learners' needs, cognitive capabilities, and different learning styles; organizing the teaching process in a constructivist manner, allowing students to participate in inquiry, discovery, reasoning, and problem-solving;

+ Flexibly applying active teaching methods and techniques; creatively combining traditional teaching methods and techniques; integrating classroom teaching activities with hands-on experiential activities, applying mathematical knowledge to real-life situations. Ensuring instructional structure balances and harmonizes core knowledge, applied knowledge, and other components.

+ Effectively and adequately utilizing teaching aids and tools as per the minimum requirements for the Mathematics subject; using self-made teaching tools that are suitable for the learning content and student audience; enhancing the use of information technology and modern teaching equipment appropriately and effectively;

- Orientation for methods of forming and developing key qualities and general competencies

+ Methods to form and develop key qualities

Through organizing learning activities, the Mathematics subject contributes along with other subjects and educational activities to help students develop honesty, a love for labor, a sense of responsibility, awareness of academic duty fulfillment; fostering confidence, interest in learning, reading habits, and a sense of inquiry and scientific discovery.

+ Methods to form and develop general competencies

++ The Mathematics subject contributes to forming and developing self-reliance and self-study abilities by training learners to choose goals, create study plans, form self-study methods, and adjust to apply them to other situations when learning mathematical concepts, knowledge, and skills, as well as when practicing or independently solving math problems and resolving mathematically significant issues.

++ The Mathematics subject contributes to forming and developing communication and collaboration skills by enabling understanding, reading comprehension, note-taking, and expressing necessary mathematical information in mathematical texts; effectively utilizing mathematical language combined with ordinary language to discuss, present mathematical contents, ideas, and solutions interactively with others, showing confidence and respect for the interlocutor when describing and explaining mathematical contents and ideas.

++ The Mathematics subject contributes to forming and developing problem-solving and creativity skills by helping students recognize problematic situations; sharing understanding of problems with others; proposing, choosing problem-solving methods and presenting solutions to the problems; evaluating implemented solutions and generalizing for similar problems.

- The teaching method of the Mathematics subject contributes to forming and developing computational competence, language competence, and other specific competencies as follows:

+ The Mathematics subject, with its distinct advantages, offers numerous opportunities to develop computational competence, reflected in providing mathematical knowledge, training computational skills, estimation, and developing elements of mathematical competence (analytic and reasoning skills, modeling abilities, problem-solving skills, communication skills, and using mathematical tools and means).

+ The Mathematics subject contributes to developing language competence by training reading comprehension skills, explaining, analyzing, evaluating mathematically significant situations, effectively utilizing mathematical language combined with ordinary language to present and describe mathematical contents, ideas, and solutions.

+ The Mathematics subject contributes to developing information technology skills by using information and communication tools and means as supporting tools in learning and self-learning; creating an experiential learning environment.

+ The Mathematics subject contributes to developing aesthetic competence by helping students become familiar with the history of mathematics, biographies of mathematicians, and recognizing the beauty of mathematics in the natural world.

>>> Download to see details of the General Education Program for Mathematics issued with Circular 32/2018/TT-BGDDT.