Digital SAT Maths -Unit 4 - 4.4 Conversion Between Radians & Degree - Study Notes- New Syllabus
Digital SAT Maths -Unit 4 – 4.4 Conversion Between Radians & Degree – Study Notes- New syllabus
Digital SAT Maths -Unit 4 – 4.4 Conversion Between Radians & Degree – Study Notes – per latest Syllabus.
Key Concepts:
Conversion Between Radians & Degrees
Conversion Between Radians & Degrees
What is a Degree?
A degree is a unit used to measure angles. A full rotation around a circle equals \( 360^\circ \).
What is a Radian?
A radian is another way to measure angles based on the radius of a circle.
One full rotation around a circle equals \( 2\pi \) radians.
Key Relationship
\( 180^\circ = \pi \text{ radians} \)
This relationship allows conversion between the two systems.
Converting Degrees to Radians
Multiply by \( \dfrac{\pi}{180} \).
\( \text{Radians} = \text{Degrees} \times \dfrac{\pi}{180} \)
Converting Radians to Degrees
Multiply by \( \dfrac{180}{\pi} \).
\( \text{Degrees} = \text{Radians} \times \dfrac{180}{\pi} \)
Common Angle Conversions
| Degrees | Radians |
|---|---|
| \( 30^\circ \) | \( \dfrac{\pi}{6} \) |
| \( 45^\circ \) | \( \dfrac{\pi}{4} \) |
| \( 60^\circ \) | \( \dfrac{\pi}{3} \) |
| \( 90^\circ \) | \( \dfrac{\pi}{2} \) |
| \( 180^\circ \) | \( \pi \) |
| \( 360^\circ \) | \( 2\pi \) |
Example 1 (Degrees to Radians):
Convert \( 120^\circ \) to radians.
▶️ Answer/Explanation
\( 120\times\dfrac{\pi}{180}=\dfrac{2\pi}{3} \)
Answer: \( \dfrac{2\pi}{3} \)
Example 2 (Radians to Degrees):
Convert \( \dfrac{5\pi}{6} \) radians to degrees.
▶️ Answer/Explanation
\( \dfrac{5\pi}{6}\times\dfrac{180}{\pi}=150^\circ \)
Answer: \( 150^\circ \)
Example 3 (Real Situation):
A wheel rotates through an angle of \( \pi \) radians. How many degrees does it rotate?
▶️ Answer/Explanation
\( \pi\times\dfrac{180}{\pi}=180^\circ \)
Answer: \( 180^\circ \)