Jumlah dan selisih dua sudut trigonometri matematika kelas XI

Summary

This educational video provides a comprehensive tutorial on solving trigonometric problems involving sum and difference of angles. The content is tailored for 11th-grade mathematics, covering formulas for sine, cosine, tangent functions, and practical examples. The video explains the application of these formulas with step-by-step solutions to problems like Sin 75°, Sin 165°, cos 105°, and Tan 105°, among others. By using special angles and simplifying the results, the presenter helps students grasp the key concepts in an easy-to-understand manner, encouraging viewers to engage with and share the content.

Takeaways

• 😀 The script introduces the topic of 'Sum and Difference of Two Trigonometric Angles' for high school math students.
• 😀 It begins with a reminder for viewers to like, subscribe, comment, and share the video.
• 😀 The formula for the sum of angles in sine is presented: Sin(α + β) = Sin(α) * Cos(β) + Cos(α) * Sin(β).
• 😀 The formula for the difference of angles in sine is also shown: Sin(α - β) = Sin(α) * Cos(β) - Cos(α) * Sin(β).
• 😀 Examples are provided to illustrate the use of these formulas, such as Sin(75°) and Sin(165°).
• 😀 For Cosine, the sum formula is Cos(α + β) = Cos(α) * Cos(β) - Sin(α) * Sin(β), and the difference formula is Cos(α - β) = Cos(α) * Cos(β) + Sin(α) * Sin(β).
• 😀 Example problems using Cosine include Cos(105°) and Cos(15°), applying the appropriate formulas for sum and difference of angles.
• 😀 The script also discusses the Tangent formulas: Tan(α + β) = (Tan(α) + Tan(β)) / (1 - Tan(α) * Tan(β)) and Tan(α - β) = (Tan(α) - Tan(β)) / (1 + Tan(α) * Tan(β)).
• 😀 Examples for Tangent are given, such as Tan(105°) and Tan(75°), showing how to break them down into known angles for easier calculation.
• 😀 The video concludes with a closing remark wishing that the tutorial is useful and encouraging further interaction from the viewers.

Q & A

What is the formula for the sum of two angles in sine?

The formula for the sum of two angles in sine is: Sin(α + β) = Sin(α) * Cos(β) + Cos(α) * Sin(β).

How do you calculate Sin(75°) using the sum of angles formula?

To calculate Sin(75°), you can break it down as Sin(30° + 45°), both of which are special angles. Using the formula for the sum of sine, the result is 1/4 * (√2 + √6).

What is the formula for the difference of two angles in sine?

The formula for the difference of two angles in sine is: Sin(α - β) = Sin(α) * Cos(β) - Cos(α) * Sin(β).

How do you calculate Sin(165°) using the difference of angles formula?

For Sin(165°), you can express it as Sin(210° - 45°). Using the difference formula, the result is 1/4 * (√6 - √2).

What is the formula for the sum of two angles in cosine?

The formula for the sum of two angles in cosine is: Cos(α + β) = Cos(α) * Cos(β) - Sin(α) * Sin(β).

How do you calculate Cos(105°) using the sum of angles formula?

To calculate Cos(105°), you can express it as Cos(60° + 45°). Using the sum of cosine formula, the result is 1/4 * (√2 - √6).

What is the formula for the difference of two angles in cosine?

The formula for the difference of two angles in cosine is: Cos(α - β) = Cos(α) * Cos(β) + Sin(α) * Sin(β).

How do you calculate Cos(15°) using the difference of angles formula?

For Cos(15°), you can express it as Cos(45° - 30°). Using the difference formula, the result is 1/4 * (√6 + √2).

What is the formula for the sum of two angles in tangent?

The formula for the sum of two angles in tangent is: Tan(α + β) = (Tan(α) + Tan(β)) / (1 - Tan(α) * Tan(β)).

How do you calculate Tan(105°) using the sum of angles formula?

To calculate Tan(105°), you can express it as Tan(60° + 45°). Using the sum of tangent formula, the result is simplified and involves rationalizing the denominator to give the final result.