Subject: Mathematics

Grade Level: Grade 9

Objective:

a. Define the six trigonometric ratios of a right triangle

b. Find the values of the six trigonometric ratios

c. Apply the trigonometric function in solving real-life problems

Learning within and across curriculum:

- Within:

1) Physics - Trigonometry is utilized in physics to calculate forces, angles, and

distances in various applications, showcasing the practicality of trigonometric
functions.

2) Geography - Trigonometry is essential in geography for measuring distances,

heights, and angles, aiding in map-making and navigation.

3) Economics - Trigonometry can be applied in economics for analyzing trends,

forecasting data, and making informed decisions using mathematical models.

ELICIT:

[Teaching Strategy: Brainstorming]

[Instructional Materials: None]

Anecdote 1 - Sharing a story about using trigonometry to determine the height of

Mayon Volcano in the Philippines.

Anecdote 2 - Using role-playing to simulate a scenario where students need to

calculate distances using trigonometric functions for a local fiesta celebration.

ENGAGE:
[Teaching Strategy: Role-Playing]

[Instructional Materials: Trigonometric tables]

1) Idea - Students will role-play as architects designing a bridge using trigonometric

ratios to ensure structural stability.

2) Idea - Interactive quiz using real-life scenarios where students must apply
trigonometric functions to solve problems related to building construction.

EXPLORE:

Activity 1: Trigonometric Treasure Hunt

[Teaching Strategy: Problem-Based Learning]

Materials - Compass, protractor, clues with trigonometric problems

Significance - Enhances problem-solving skills and reinforces understanding of

trigonometric ratios

Instructions -

1) Students follow clues to locate hidden treasures using trigonometry.

2) Solve trigonometric problems at each treasure location.

3) Rubric

- Accuracy of solutions - 15 pts.

- Efficiency in solving problems - 10 pts.

- Collaboration with team members - 10 pts.

Assessment Questions:

1) Calculate the sine of angle A in a triangle with sides 5, 12, and 13.

2) Find the tangent of angle X in a right triangle with opposite side 7 and adjacent
side 24.

3) Determine the cosine of angle Y in a triangle with hypotenuse 10 and opposite

side 6.
Activity 2: Trigonometric Art Project

[Teaching Strategy: Project-Based Learning]

Materials - Construction paper, rulers, colored markers

Significance - Integrates creativity with trigonometry concepts

Instructions -

1) Create geometric shapes using trigonometric ratios to determine angles and side
lengths.

2) Design an art piece showcasing different trigonometric functions.

3) Rubric

- Creativity in design - 15.

- Accuracy of angles and measurements - 10 pts.

- Presentation of trigonometric concepts - 10 pts.

Assessment Questions:

1) How can you use trigonometry to create a visually appealing geometric design?

2) Explain the relationship between trigonometric ratios and the angles in your
artwork.

3) Demonstrate how trigonometry can be applied in creating symmetrical patterns.

Inclusive Activity 3: Trigonometric Scavenger Hunt

[Teaching Strategy: Cooperative Learning]

Materials - None

Significance - Promotes teamwork and problem-solving without the need for

additional resources

Instructions -

1) Students work in groups to solve trigonometric problems scattered around the

classroom or school premises.

2) Each correct answer leads to the next clue, encouraging collaboration and critical
thinking.

3) Rubric

- Accuracy of solutions - 15 pts.

- Teamwork and cooperation - 10 pts.

- Time efficiency in completing the hunt - 10 pts.

Assessment Questions:

1) Find the value of the cosine of angle Z in a triangle with adjacent side 15 and
hypotenuse 17.

2) Calculate the tangent of angle B in a right triangle with opposite side 5 and
adjacent side 12.

3) Determine the sine of angle C in a triangle with sides 8, 15, and 17.

EXPLAIN:

Activity 1 - Students will engage in a trigonometric treasure hunt, applying their

knowledge of ratios to solve real-world problems and enhance their critical thinking
skills.

Activity 2 - Through a trigonometric art project, students will visually represent

trigonometric concepts, reinforcing their understanding of angles and side
relationships.

Promote further discussion with online references using the following:

Objective: a. define the six trigonometric ratio of right triangle;

The six trigonometric ratios of a right triangle are defined as follows: 1. Sine (sin)
ratio: sin = opposite/hypotenuse 2. Cosine (cos) ratio: cos = adjacent/hypotenuse 3.
Tangent (tan) ratio: tan = opposite/adjacent 4. Cosecant (csc) ratio: csc = 1/sin 5.
Secant (sec) ratio: sec = 1/cos 6. Cotangent (cot) ratio: cot = 1/tan These ratios are
used to relate the angles of a right triangle to the lengths of its sides.

Right triangles & trigonometry | Math | Khan Academy

Monthly. Yearly. Trigonometry 4 units · 36 skills. Unit 1 Right triangles &

trigonometry. Unit 2 Trigonometric functions. Unit 3 Non-right triangles &
trigonometry. Unit 4 Trigonometric equations and identities. Course challenge. Test
your knowledge of the skills in this course....

Source: https://www.khanacademy.org/math/trigonometry/trigonometry-right-
triangles

4.1.2: Right Triangles and Trigonometric Ratios

There are two special triangles that will be important in what follows where the ratios
are known exactly (in terms of square roots). First, consider an isosceles right
triangle: We can use the Pythagorean Theorem to find that the hypotenuse is 2-√ 2.
So, for example, cos45o = 1 2-√ = 2-√ 2 cos. ⁡. ...

Source:
https://math.libretexts.org/Courses/City_University_of_New_York/College_Algebra_a
nd_Trigonometry-_Expressions_Equations_and_Graphs/
04:_Introduction_to_Trigonometry_and_Transcendental_Expressions/
4.01:_Trigonometric_Expressions/
4.1.02:_Right_Triangles_and_Trigonometric_Ratios

Objective: b. find the values of the six trigonometric ratios; and

To find the values of the six trigonometric ratios, you can use trigonometric identities
to calculate them. The six trigonometric ratios are sine, cosine, tangent, cosecant,
secant, and cotangent. You can determine these values based on the relationships
between sine, cosine, and tangent using the following formulas: - Tangent (tan) is
the sine-to-cosine ratio: tan(α) = sin(α)/cos(α) - Cosecant (csc) is the reciprocal of
the sine: csc(α) = 1/sin(α) By knowing the values of sine and cosine, you can
calculate the values of tangent, cosecant, secant, and cotangent using these
trigonometric identities.

Trig Calculator | Trigonometric Calculator

Tan, cot, sec, and csc, calculated from trig identities. Once you know the value of
sine and cosine, you can use the following trigonometric identities to obtain the
values of the other four functions: Tangent is the sine-to-cosine ratio. tan(α) =
sin(α)/cos(α) Cosecant is the reciprocal of the sine...

Source: https://www.omnicalculator.com/math/trig

Trigonometric Ratios (Definition, Formulas, Examples) - BYJU'S

The Six trigonometric ratios are sine, cosine, tangent, secant, cosecant and
cotangent. ... From this table, we can find the value for the trigonometric ratios for
these angles. Examples are: ... January 31, 2020 at 7:33 am. Tnks for this! Very
informative! Reply. RANI S MARTIN. December 23, 2021 at...

Source: https://byjus.com/maths/trigonometric-ratios/
Objective: c. aapply the trigonometric function in solving real-life
problems.

Trigonometric functions are commonly applied in solving real-life problems across

various fields such as architecture, construction, communications, electrical
engineering, flight, GPS, graphics, land surveying, music, tides, optics, and
trajectories. These functions play a crucial role in indirect measurement, enabling
calculations for unknown measurements that are otherwise impossible to obtain
directly. The applications of trigonometry extend to everyday scenarios, offering
solutions to a wide range of practical problems by leveraging the principles of
triangle ratios, angles, and lengths.

2.2.5: Applications of Inverse Trigonometric Functions

The following problems are real-world problems that can be solved using the
trigonometric functions. In everyday life, indirect measurement is used to obtain
answers to problems that are impossible to solve using measurement tools.
However, mathematics will come to the rescue in the form of trigonom...

Source:
https://k12.libretexts.org/Bookshelves/Mathematics/Trigonometry/02:_Trigonometric_
Ratios/2.02:_Solving_Triangles/
2.2.05:_Applications_of_Inverse_Trigonometric_Functions

Applications of Trigonometric Functions - Video Tutorials & Practice ...

Learn Applications of Trigonometric Functions with free step-by-step video

explanations and practice problems by experienced tutors. ... Algebraic Expressions,
Mathematical Models, and Real Numbers. Exponents and Scientific Notation.
Radicals and Rational Exponents ... Trigonometry Word Problem, Fin...

Source: https://www.pearson.com/channels/precalculus/explore/trigonometric-
functions/applications-of-trigonometric-functions

ELABORATE:
[Teaching Strategy: Problem-Based Learning]

Task 1 - Students will measure the angles and distances in their school courtyard
using trigonometric functions and create a scale model based on their calculations.

Task 2 - Students will design a survey questionnaire for a real-life scenario where
trigonometric functions can be used to collect and analyze data for decision-making
processes.

Supporting Material 1 - A article on how trigonometry is used in architecture to

design structurally sound buildings.

Supporting Material 2 - A case study on how trigonometric functions are applied in

surveying land for urban development projects.

EVALUATE:

[Teaching Strategy: Inquiry-Based Learning]

[Instructional Materials: Trigonometric calculators]

Question 1 - Determine the value of the tangent of angle A in a right triangle with
opposite side 3 and adjacent side 4.

Question 2 - Calculate the cosine of angle B in a triangle with hypotenuse 10 and

opposite side 6.

Question 3 - Find the sine of angle X in a triangle with sides 9, 12, and 15.
H.O.T.S.:

Question 1 - How can trigonometric ratios be used to solve problems involving

heights and distances in real-world applications?

Answer 1 - Trigonometric ratios help in calculating unknown lengths or angles in

triangles, aiding in various fields such as engineering, physics, and architecture.

Question 2 - Why is it important to understand the relationship between trigonometric

functions and right triangles in practical situations?

Answer 2 - Understanding trigonometric functions in right triangles allows individuals

to accurately measure and analyze spatial relationships, crucial for accurate
calculations in construction, navigation, and surveying.

Question 3 - Explain how trigonometry can be utilized to solve complex problems

beyond basic triangle calculations.

Answer 3 - Trigonometry extends to advanced applications like satellite

communication, oceanography, and astronomy, where precise calculations using
trigonometric functions are essential for accurate data analysis.

EXTEND:

[Teaching Strategy: Experiential Learning]

[Instructional Materials: Real-world scenarios]

Use-case 1 - Students will use trigonometric functions to determine the optimal angle
for launching a rocket into space, considering factors such as velocity and trajectory.

Use-case 2 - Applying trigonometric ratios, students will analyze the angles and
distances involved in designing a sustainable urban transportation system,
considering traffic flow and efficiency.

Assignment:

1) Design a blueprint for a building structure using trigonometric functions to

calculate angles and side lengths. Include an explanation of how trigonometry is
essential in architectural design.

2) Conduct a survey in your community to gather data on angles and distances, then
apply trigonometric functions to analyze the collected information and present your
findings in a report format.
REFERENCES:

Right triangles & trigonometry | Math | Khan Academy

https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles

4.1.2: Right Triangles and Trigonometric Ratios

https://math.libretexts.org/Courses/City_University_of_New_York/College_Algebra_a
nd_Trigonometry-_Expressions_Equations_and_Graphs/
04:_Introduction_to_Trigonometry_and_Transcendental_Expressions/
4.01:_Trigonometric_Expressions/
4.1.02:_Right_Triangles_and_Trigonometric_Ratios

Trig Calculator | Trigonometric Calculator https://www.omnicalculator.com/math/trig

Trigonometric Ratios (Definition, Formulas, Examples) - BYJU'S

https://byjus.com/maths/trigonometric-ratios/

2.2.5: Applications of Inverse Trigonometric Functions

https://k12.libretexts.org/Bookshelves/Mathematics/Trigonometry/02:_Trigonometric_
Ratios/2.02:_Solving_Triangles/
2.2.05:_Applications_of_Inverse_Trigonometric_Functions

Applications of Trigonometric Functions - Video Tutorials & Practice ...

https://www.pearson.com/channels/precalculus/explore/trigonometric-functions/
applications-of-trigonometric-functions

IMAGES:
END OF REFERENCES: