Apa itu Sudut Istimewa - Segitiga siku siku #04

Summary

The video explains special angles in trigonometry, highlighting those whose sine and cosine values can be determined easily without calculators. Key angles include 0°, 30°, 45°, 60°, 90°, 180°, 270°, and their respective values in all quadrants. The speaker emphasizes the importance of remembering these angles and explains how to determine if an angle, such as 220°, is special by calculating the difference from the nearest axis. The lesson concludes with a reminder to like, share, and subscribe to the channel.

Takeaways

• 😀 Special angles are those whose trigonometric ratios can be determined without a calculator or tables.
• 😀 The primary special angles are 0°, 30°, 45°, 60°, 90°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, and 360°.
• 😀 The angles that serve as axes on the Cartesian diagram include 0° (or 360°), 90°, 180°, and 270°.
• 😀 In the first quadrant, the special angles include 30°, 45°, and 60°, which are fundamental for other quadrants.
• 😀 Special angles in the second quadrant can be obtained by adding 90° to 30°, 45°, and 60°.
• 😀 In the third quadrant, special angles are found by adding 180° to 30°, 45°, and 60°.
• 😀 The fourth quadrant special angles result from adding 270° to 30°, 45°, and 60°.
• 😀 The angle 220° is greater than 180° but less than 270°, placing it in the third quadrant.
• 😀 To determine if an angle like 220° is a special angle, calculate the difference from the nearest x-axis, which is 180° in this case.
• 😀 A difference of 0°, 30°, 45°, 60°, or 90° indicates that the angle is special; however, 220° has a difference of 40°, confirming it is not a special angle.

Q & A

What are special angles in trigonometry?

Special angles are angles whose sine and cosine values can be determined easily without using a calculator or tables.

Which angles are considered special angles on the Cartesian plane?

The special angles on the Cartesian plane are 0 degrees (or 360 degrees), 90 degrees, 180 degrees, and 270 degrees.

What are the special angles in the first quadrant?

The special angles in the first quadrant are 30 degrees, 45 degrees, and 60 degrees.

How are special angles in other quadrants derived from those in the first quadrant?

Special angles in the second quadrant can be obtained by adding 90 degrees to 30, 45, and 60 degrees. In the third quadrant, they are derived by adding 180 degrees to these angles. In the fourth quadrant, they are derived by adding 270 degrees.

What is the list of all special angles mentioned in the script?

The special angles are 0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, and 360 degrees.

How can we determine if an angle, like 220 degrees, is a special angle?

To determine if an angle is special, calculate the difference between the angle and the nearest x-axis angle. If the difference is 0, 30, 45, 60, or 90 degrees, then it is a special angle.

What is the difference between 220 degrees and the nearest x-axis angle?

The difference between 220 degrees and the nearest x-axis angle, which is 180 degrees, is 40 degrees.

Does the angle 220 degrees qualify as a special angle?

No, since the difference is 40 degrees, which is not one of the designated special angle differences.

What is the significance of remembering special angles in trigonometry?

Remembering special angles is crucial because they serve as the foundation for understanding trigonometric functions and calculations in various quadrants.

What action does the speaker encourage at the end of the video?

The speaker encourages viewers to like, share, and subscribe to the channel.