Sum and Difference Identities & Formulas - Sine, Cosine, Tangent - Degrees & Radians, Trigonometry

Summary

This video explains the sum and difference trigonometric identities, focusing on sine, cosine, and tangent functions. It demonstrates how to apply these formulas to evaluate specific angles like 75°, 15°, and 7π/12. The video also includes practical examples of converting radians to degrees, simplifying complex trigonometric expressions, and using special triangles (30-60-90 and 45-45-90) for reference. Emphasis is placed on the use of the unit circle and rationalizing expressions, particularly for tangent. The video aims to equip viewers with the tools to solve a variety of trigonometric problems effectively.

Takeaways

• 😀 Sine sum formula: sin(A + B) = sin(A)cos(B) + cos(A)sin(B) helps simplify trigonometric calculations.
• 😀 Sine difference formula: sin(A - B) = sin(A)cos(B) - cos(A)sin(B) is essential for solving problems involving angle differences.
• 😀 To calculate sin(75°), split the angle into two common angles (30° + 45°) and apply the sine sum formula.
• 😀 Special right triangles (30-60-90 and 45-45-90) are useful for deriving values of sine, cosine, and tangent for common angles.
• 😀 Understanding the unit circle is crucial for evaluating trigonometric functions like sine, cosine, and tangent.
• 😀 Cosine sum formula: cos(A + B) = cos(A)cos(B) - sin(A)sin(B) is useful for calculating cosines of angle sums.
• 😀 Tangent sum and difference formulas allow you to evaluate tangent of angle sums or differences, e.g., tan(A + B) and tan(A - B).
• 😀 For example, to calculate sin(15°), use the sine difference formula since 15° = 45° - 30°.
• 😀 Converting radians to degrees (e.g., 7π/12 to 105°) helps simplify trigonometric evaluations involving radians.
• 😀 Rationalizing complex fractions, especially when dealing with tangent, is a necessary skill for simplifying expressions.

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