Summary of CÍRCULO TRIGONOMÉTRICO -

Main Ideas and Concepts

• Trigonometric Circle Construction:

  The video demonstrates how to construct a trigonometric circle using a Protractor and Ruler. The circle is divided into 360 degrees, with key points marked at every 30 degrees and 45 degrees.

• Quadrants of the Circle:

  The circle is divided into four quadrants:

  • First Quadrant: 0° to 90°
  • Second Quadrant: 90° to 180°
  • Third Quadrant: 180° to 270°
  • Fourth Quadrant: 270° to 360°

  Each quadrant has distinct properties for trigonometric functions.

• Trigonometric Ratios:

  The Sine, Cosine, and Tangent functions are defined in relation to the unit circle. The values of these functions vary depending on the quadrant:

  • Sine: Positive in the first and second quadrants; negative in the third and fourth.
  • Cosine: Positive in the first and fourth quadrants; negative in the second and third.
  • Tangent: Positive in the first and third quadrants; negative in the second and fourth.
• Conversion Between Degrees and Radians:

  The video explains how to convert angles from Degrees to Radians using the relationship \( \pi \text{ rad} = 180° \). Examples are provided for converting common angles (30°, 45°, 60°, etc.).

• Finding Values of Sine, Cosine, and Tangent:

  Techniques for finding the values of Sine, Cosine, and Tangent for angles in different quadrants by relating them to known angles in the first quadrant. Use of symmetry and reference angles to determine signs and values.

Methodology and Instructions

• Constructing the Trigonometric Circle:
  1. Draw a circle and two perpendicular lines (axes).
  2. Use a Protractor to mark 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, 330°, and 360°.
  3. Mark additional angles at 45° intervals.
• Finding Sine, Cosine, and Tangent Values:
  1. Identify the quadrant in which the angle lies.
  2. Relate the angle to a known angle in the first quadrant.
  3. Determine the sign based on the quadrant:
     • First Quadrant: All positive.
     • Second Quadrant: Sine positive, Cosine negative.
     • Third Quadrant: Sine and Cosine negative.
     • Fourth Quadrant: Sine negative, Cosine positive.
  4. Use the known values of Sine, Cosine, and Tangent from the first quadrant to find the desired values.

Speakers or Sources Featured

The video appears to be presented by an unnamed instructor (referred to as "teacher" or "professor") who provides explanations and demonstrations throughout the lesson.

Notable Quotes

— 00:12 — « I like to take breakfast with bread. »

— 03:02 — « Dog treats are the greatest invention ever. »

Category

Educational

Video