BAB TRIGONOMETRI | SUDUT, UKURAN SUDUT DALAM DERAJAT & RADIAN

Summary

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Takeaways

• 😀 Understanding the relationship between degrees and radians is essential for angle conversions.
• 😀 The conversion formula from degrees to radians is θ (radians) = θ (degrees) × (π/180).
• 😀 To convert radians to degrees, the formula is θ (degrees) = θ (radians) × (180/π).
• 😀 One full circle (360°) corresponds to 2π radians.
• 😀 The relationship between radians and degrees allows for easier calculations in geometry and trigonometry.
• 😀 To convert 150° to radians, the result is 5π/6 radians.
• 😀 240° in radians is equivalent to 4π/3 radians.
• 😀 For radians to degrees, 1/3 π radians is equal to 60°.
• 😀 2/5 π radians converts to 72° when applying the conversion formula.
• 😀 Key takeaway: Both degree-to-radian and radian-to-degree conversions involve multiplying by specific ratios involving π.
• 😀 Practice with multiple examples is crucial to mastering conversions between radians and degrees.

Q & A

What is the formula to convert degrees to radians?

The formula to convert degrees to radians is: Radian = (Degree × π) / 180.

What is the formula to convert radians to degrees?

The formula to convert radians to degrees is: Degree = (Radian × 180) / π.

How do you convert 150° into radians?

To convert 150° to radians: (150 × π) / 180 = 5π / 6 radians.

What is the value of 240° in radians?

To convert 240° to radians: (240 × π) / 180 = 4π / 3 radians.

How would you convert 1/3 radians to degrees?

To convert 1/3 radians to degrees: (1/3 × 180) = 60°.

How do you convert 2/5 radians into degrees?

To convert 2/5 radians to degrees: (2/5 × 180) = 72°.

Why is the value of 1 degree equal to π/180 radians?

1 degree is equal to π/180 radians because the full circle is 360°, which is equivalent to 2π radians. Thus, 1 degree is 2π/360 = π/180 radians.

What is the relation between degrees and radians?

The relationship between degrees and radians is that 180° equals π radians. Therefore, to convert between the two, you multiply by π/180 for degrees to radians, and by 180/π for radians to degrees.

How do you simplify the conversion between degrees and radians?

To simplify the conversion between degrees and radians, multiply the degree value by π/180 to convert to radians, or multiply the radian value by 180/π to convert to degrees.

What does it mean if an angle is expressed in radians?

An angle expressed in radians means the angle is measured based on the radius of the circle. One radian is the angle subtended by an arc whose length is equal to the radius of the circle.