trigonometri // cara mudah menghitung trigonometri di kuadran 1,2,3,4

Summary

This video tutorial explains an easy method to calculate trigonometric values in all four quadrants. It introduces the mnemonic ‘old Sin, Tan, Cos’ to help remember which trigonometric functions are positive in each quadrant. The video covers key concepts like special angle values (0° to 90°), and demonstrates how to use simple formulas to solve problems in each quadrant. It provides clear examples for Sin, Cos, and Tan in Quadrants 1 to 4, making trigonometry easier to understand and apply in practice.

Takeaways

• 😀 Quadrant I: All trigonometric functions (sin, cos, tan) are positive.
• 😀 Quadrant II: Only sine is positive, while cosine and tangent are negative.
• 😀 Quadrant III: Only tangent is positive, while sine and cosine are negative.
• 😀 Quadrant IV: Only cosine is positive, while sine and tangent are negative.
• 😀 The 'Old Sin, Tan, Cos' formula helps in memorizing which functions are positive in each quadrant.
• 😀 Special angles for sine: 0°, 30°, 45°, 60°, and 90° with corresponding values: 0, 1/2, √2/2, √3/2, and 1.
• 😀 Special angles for cosine: 0°, 30°, 45°, 60°, and 90° with corresponding values: 1, √3/2, √2/2, 1/2, and 0.
• 😀 Special angles for tangent: 0°, 30°, 45°, 60°, and 90° with corresponding values: 0, 1/√3, 1, √3, and infinity.
• 😀 For angles in Quadrant II, use the formula 180° - alpha to find the reference angle.
• 😀 For angles in Quadrant III, use the formula 180° + alpha to find the reference angle.
• 😀 For angles in Quadrant IV, use the formula 360° - alpha to find the reference angle.

Q & A

What is the key method for memorizing the signs of trigonometric functions in different quadrants?

The key method is to use the acronym 'Old Sin, Tan Cos' to remember the signs of the trigonometric functions in each quadrant.

What trigonometric functions are positive in Quadrant 1?

In Quadrant 1, all trigonometric functions—sine (sin), cosine (cos), and tangent (tan)—are positive.

In Quadrant 2, which trigonometric function is positive?

In Quadrant 2, only sine (sin) is positive. Cosine (cos) and tangent (tan) are negative.

How can you quickly determine the value of sin, cos, and tan in Quadrant 3?

In Quadrant 3, tangent (tan) is positive, while sine (sin) and cosine (cos) are negative.

What about Quadrant 4? Which trigonometric function is positive?

In Quadrant 4, cosine (cos) is positive, while sine (sin) and tangent (tan) are negative.

How do you use your fingers to remember special angles for sine and cosine?

You can use your fingers to remember special angles from 0° to 90° with values for sine and cosine: 0°, 30°, 45°, 60°, and 90°. The sine and cosine values for these angles are 0, 1/2, √2/2, √3/2, and 1.

How can you quickly calculate the value of sine, cosine, or tangent in different quadrants?

For Quadrant 2, subtract the angle from 180°. For Quadrant 3, add the angle to 180°. For Quadrant 4, subtract the angle from 360°.

What is the value of sin 45° in Quadrant 1?

Since 45° is in Quadrant 1, where all values are positive, sin 45° equals √2/2.

How do you calculate sin 120° using the method for Quadrant 2?

For sin 120°, since 120° is in Quadrant 2, you subtract 120° from 180°, which gives you 60°. Therefore, sin 120° equals sin 60°, which is √3/2.

Why is cos 210° negative?

Cos 210° is in Quadrant 3, where cosine is negative. The angle 210° corresponds to an angle of 30° in the reference triangle, so cos 210° equals -cos 30°, which is -√3/2.