(Part 2) Nilai Fungsi Trigonometri || Matematika Tingkat Lanjut Kelas XI

Summary

This video provides a detailed lesson on advanced trigonometry for 11th-grade students. It covers how to determine the values of trigonometric functions across different quadrants, including the 2nd, 3rd, and 4th quadrants, as well as for angles greater than 360° and less than 0°. The video explains the concepts using examples and formulas, emphasizing the importance of recognizing positive and negative values in each quadrant. The lesson is designed to help students understand and apply these principles in solving trigonometric problems.

Takeaways

• 😀 The video focuses on advanced mathematics, specifically trigonometry for 11th grade students.
• 😀 The main goal of the lesson is to teach how to determine the values of trigonometric functions in different quadrants and for angles greater or less than 360 degrees.
• 😀 In the second quadrant, only sine (sin) is positive, while cosine (cos) and tangent (tan) are negative.
• 😀 The formula for determining trigonometric functions in the second quadrant is 180° - θ.
• 😀 An example is provided for sin(120°) in the second quadrant, where the angle is 180° - 60°, making sin(120°) equal to 1/2√3.
• 😀 In the third quadrant, only tangent (tan) is positive, while sine (sin) and cosine (cos) are negative.
• 😀 The formula for determining trigonometric functions in the third quadrant is 180° + θ.
• 😀 An example for sin(210°) is given, showing the process of determining the angle (180° + 30°) and the corresponding trigonometric values.
• 😀 In the fourth quadrant, only cosine (cos) is positive, while sine (sin) and tangent (tan) are negative, and the formula used is 360° - θ.
• 😀 The video also addresses angles larger than 360° and smaller than 0°, showing how to reduce the angles to their equivalent within the 0° to 360° range by using multiples of 360°.

Q & A

What is the main topic of the video?

The main topic of the video is advanced trigonometry for 11th-grade students, focusing on determining the values of trigonometric functions in different quadrants and for angles greater or less than 360°.

What are the five learning objectives of this video?

The five learning objectives are: 1) Determining the values of trigonometric functions in the second quadrant. 2) Determining the values of trigonometric functions in the third quadrant. 3) Determining the values of trigonometric functions in the fourth quadrant. 4) Determining the values of trigonometric functions for angles greater than 360°. 5) Determining the values of trigonometric functions for angles less than 360°.

How do you find the values of trigonometric functions in the second quadrant?

In the second quadrant, the angle is between 90° and 180°. The formula to find the values is 180° - θ. In this quadrant, only sine (sin) is positive, while cosine (cos) and tangent (tan) are negative.

Can you provide an example of finding sine, cosine, and tangent for an angle in the second quadrant?

Yes. For example, for sin(120°), since 120° is in the second quadrant, we calculate 180° - 60° = 120°. Sin is positive, so sin(120°) = √3/2. For cos(120°), cos is negative, so cos(120°) = -1/2. For tan(120°), tan is also negative, so tan(120°) = -√3.

How do you find trigonometric function values in the third quadrant?

In the third quadrant, the angle is between 180° and 270°. The formula to find the values is 180° + θ. In this quadrant, only tangent (tan) is positive, while sine (sin) and cosine (cos) are negative.

Can you give an example of how to find trigonometric values in the third quadrant?

For example, for sin(210°), since 210° is in the third quadrant, we calculate 180° + 30° = 210°. Sin is negative, so sin(210°) = -1/2. For cos(210°), cos is negative, so cos(210°) = -1/2√3. For tan(210°), tan is positive, so tan(210°) = 1/√3.

How do you find the trigonometric function values in the fourth quadrant?

In the fourth quadrant, the angle is between 270° and 360°. The formula to find the values is 360° - θ. In this quadrant, only cosine (cos) is positive, while sine (sin) and tangent (tan) are negative.

Can you explain how to find the sine, cosine, and tangent for an angle in the fourth quadrant?

For example, for cos(330°), since 330° is in the fourth quadrant, we calculate 360° - 30° = 330°. Cos is positive, so cos(330°) = √3/2. For sin(330°), sin is negative, so sin(330°) = -1/2. For tan(330°), tan is negative, so tan(330°) = -1/√3.

What if the angle is greater than 360°? How do you find the trigonometric values?

When the angle is greater than 360°, subtract multiples of 360° until the angle falls between 0° and 360°. Then, use the same quadrant rules and formulas to find the trigonometric values. For example, for 945°, subtract 2 * 360° to get 225°, and then find the trigonometric values for 225°.

How do you handle negative angles when determining trigonometric values?

For negative angles, add or subtract multiples of 360° to get the equivalent positive angle. Then, apply the quadrant rules. For example, for -1110°, subtract 3 * 360° to get -30°, and find the trigonometric values for -30°.