Convert (A) 150° into radians (B) (3pi)/4 into degree

To solve these conversions, let's break them down step by step:

### (A) Convert \( 150^\circ \) into radians

The conversion formula from degrees to radians is:

\[
\text{Radians} = \left(\frac{\pi}{180^\circ}\right) \times \text{Degrees}
\]

So, for \( 150^\circ \):

\[
\text{Radians} = \left(\frac{\pi}{180^\circ}\right) \times 150^\circ = \frac{150\pi}{180} = \frac{5\pi}{6}
\]

Thus, \( 150^\circ \) is equivalent to \( \frac{5\pi}{6} \) radians.

### (B) Convert \( \frac{3\pi}{4} \) into degrees

The conversion formula from radians to degrees is:

\[
\text{Degrees} = \left(\frac{180^\circ}{\pi}\right) \times \text{Radians}
\]

So, for \( \frac{3\pi}{4} \):

\[
\text{Degrees} = \left(\frac{180^\circ}{\pi}\right) \times \frac{3\pi}{4} = \frac{3 \times 180^\circ}{4} = 135^\circ
\]

Thus, \( \frac{3\pi}{4} \) radians is equivalent to \( 135^\circ \).

Would you like further details or have any questions?

Here are 5 related questions:
1. Convert \( 210^\circ \) into radians.
2. Convert \( \frac{\pi}{3} \) into degrees.
3. What is \( 360^\circ \) in radians?
4. Convert \( \frac{7\pi}{6} \) into degrees.
5. Convert \( 45^\circ \) into radians.

**Tip:** Remember that \( \pi \) radians is always equivalent to \( 180^\circ \), which is the key factor in converting between degrees and radians.

Explore detailed solutions for converting 150 degrees to radians and 3pi/4 radians to degrees. Understand the conversion formulas and methods used in trigonometry. Suitable for advanced high school students and anyone interested in trigonometric conversions.

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