TR-15: Sine and Cosine of Common Angles (Trigonometry series by Dennis F. Davis)

Introduction

This tutorial focuses on understanding the sine and cosine values for common angles, which are essential for mastering trigonometry. By using a mnemonic technique, you'll be able to recall these values effortlessly, making it easier to apply them in various mathematical contexts, such as in exams or practical applications.

Step 1: Understanding Sine and Cosine

• Definition: Sine (sin) and cosine (cos) are fundamental trigonometric functions related to the angles of a right triangle.
• Common Angles: The angles you need to memorize include:
  • 0 degrees
  • 30 degrees
  • 45 degrees
  • 60 degrees
  • 90 degrees

Step 2: Memorizing Values with a Mnemonic

• Mnemonic Introduction: To simplify memorization, use the Large, Medium, Small (LMS) mnemonic.

• Values:

  • For sine (sin):
    • 0°: sin(0) = 0
    • 30°: sin(30) = 1/2
    • 45°: sin(45) = √2/2
    • 60°: sin(60) = √3/2
    • 90°: sin(90) = 1
  • For cosine (cos):
    • 0°: cos(0) = 1
    • 30°: cos(30) = √3/2
    • 45°: cos(45) = √2/2
    • 60°: cos(60) = 1/2
    • 90°: cos(90) = 0

• Application of the Mnemonic:

  • Think of the mnemonic as representing the size and order of the angle values.
  • For example, as the angle increases from 0° to 90°, the sine value increases while the cosine value decreases.

Step 3: Practice with Angle Values

• Exercises: To reinforce your understanding, practice determining sine and cosine values for the angles listed above:
  • Write down each angle and its corresponding sine and cosine value.
  • Use flashcards to test yourself.

Step 4: Further Learning Resources

• Extra Problems and Drills: For additional practice, watch the extra drills video TR-15X to solidify your skills.
• Proof of Values: If you're interested in the derivation of these sine and cosine values, check out the optional video TR-15Z.

Conclusion

Knowing the sine and cosine values for common angles is crucial for success in trigonometry. By utilizing the Large, Medium, Small mnemonic, you can easily recall these values, enhancing your problem-solving skills. Continue practicing with exercises and explore additional resources for a deeper understanding. Remember, consistent practice is key to mastering trigonometric concepts!