Navigating Trigonometry on the Coordinate Plane

Algebra 2 Grades High School 10:43 Video
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Lesson Description

Mastering trigonometric functions using quadrant diagrams. Students will learn to construct triangles on the coordinate plane and apply trigonometric ratios to solve problems. This lesson will help students understand how trigonometry works in the four quadrants.

Video Resource

Quadrant Diagram Triangle

Kevinmathscience

Duration: 10:43
Watch on YouTube

Key Concepts

  • Quadrant Diagram
  • Trigonometric Ratios (SOH CAH TOA)
  • Pythagorean Theorem
  • Reference Angles

Learning Objectives

  • Students will be able to draw triangles correctly in a quadrant diagram based on a given point.
  • Students will be able to apply the Pythagorean theorem to find the missing side of a triangle.
  • Students will be able to calculate trigonometric ratios (sin, cos, tan, csc, sec, cot) in different quadrants.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the coordinate plane and the four quadrants. Briefly recap the basic trigonometric ratios (SOH CAH TOA).
  • Video Viewing (10 mins)
    Play the video 'Quadrant Diagram Triangle' by Kevinmathscience. Instruct students to take notes on the key steps and examples provided.
  • Triangle Construction (15 mins)
    Guide students through constructing triangles in each quadrant. Emphasize drawing the triangle to the x-axis. Provide example points and have students draw the corresponding triangles.
  • Applying Trigonometry (15 mins)
    Work through examples of finding sin, cos, tan, csc, sec, and cot in different quadrants. Emphasize the importance of signs (+/-) based on the quadrant.
  • Practice Problems (10 mins)
    Assign practice problems where students must draw triangles, find side lengths, and calculate trigonometric ratios. Have them check their work.

Interactive Exercises

  • Quadrant Challenge
    Divide students into groups. Give each group a set of coordinates. Each group must draw the triangle on a whiteboard, calculate all trigonometric ratios, and explain their process.
  • Online Trigonometry Calculator Practice
    Use an online trigonometry calculator to practice problems similar to what was taught in the video.

Discussion Questions

  • Why is it important to always draw the triangle to the x-axis?
  • How do the signs of x and y coordinates affect the signs of the trigonometric ratios in each quadrant?
  • Explain how the Pythagorean theorem is used in this context.

Skills Developed

  • Spatial Reasoning
  • Problem-Solving
  • Trigonometric Application

Multiple Choice Questions

Question 1:

In a quadrant diagram, which axis should you always draw your triangle to?

Correct Answer: X-axis

Question 2:

If a point is located in Quadrant III, what are the signs of its x and y coordinates?

Correct Answer: x: -, y: -

Question 3:

Which trigonometric function is defined as opposite/hypotenuse?

Correct Answer: Sine

Question 4:

Which trigonometric function is the inverse of cosine?

Correct Answer: Secant

Question 5:

What is the Pythagorean Theorem?

Correct Answer: a² + b² = c²

Question 6:

If the adjacent side of an angle is 4 and the hypotenuse is 5, what is the cosine of the angle?

Correct Answer: 4/5

Question 7:

In which quadrant is sine positive and cosine negative?

Correct Answer: Quadrant II

Question 8:

What is the reciprocal of the tangent function?

Correct Answer: Cotangent

Question 9:

What is the value of the hypotenuse if the opposite side is 8 and the adjacent side is 6?

Correct Answer: 10

Question 10:

If sin(θ) = 3/5, what is csc(θ)?

Correct Answer: 5/3

Fill in the Blank Questions

Question 1:

The longest side of a right triangle is called the ________.

Correct Answer: hypotenuse

Question 2:

The trigonometric function _____ is defined as opposite over adjacent.

Correct Answer: tangent

Question 3:

In quadrant II, the x-coordinate is _____ and the y-coordinate is _____.

Correct Answer: negative, positive

Question 4:

The acronym used to remember the trigonometric ratios is ________.

Correct Answer: SOH CAH TOA

Question 5:

The side adjacent to an angle is always _______ to the angle

Correct Answer: next

Question 6:

The inverse of the sine function is the ______ function.

Correct Answer: cosecant

Question 7:

To find the missing side of a triangle, use the ________.

Correct Answer: Pythagorean theorem

Question 8:

If cos(θ) = adjacent/hypotenuse, then sec(θ) = ______/_______.

Correct Answer: hypotenuse, adjacent

Question 9:

The angle between the x-axis and hypotenuse is know as the ______ angle.

Correct Answer: reference

Question 10:

If tan(θ) = 1, then cot(θ) = _____.

Correct Answer: 1

Educational Standards

A2.F.1.1:Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain. A2.F.1.2:Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [𝑓(𝑥 + 𝑐), 𝑓(𝑥) + 𝑐, 𝑓(𝑐𝑥), and 𝑐𝑓(𝑥)] algebraically and graphically.

Teaching Materials

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