Convert each of the following angles shown in radians to degrees. Give your answer correct to 1 d.p. (a) 3c (b) 4c (c) 1.2c (d) 0.56c

Step 1: Convert $45^\circ$ to radians.

To convert degrees to radians, use the formula
$\theta_radians = \theta_degrees \times \frac{\pi}{180}.$

Substitute $45^\circ$:
$45^\circ \times \frac{\pi}{180} = \frac{45\pi}{180}.$

Simplify the fraction:
$\frac{45\pi}{180} = \frac{\pi}{4}.$

$\boxed{\dfrac{\pi}{4}}$ radians

Step 2: Convert $30^\circ$ to radians.

Use the formula
$\theta_radians = \theta_degrees \times \frac{\pi}{180}.$

Substitute $30^\circ$:
$30^\circ \times \frac{\pi}{180} = \frac{30\pi}{180}.$

Simplify the fraction:
$\frac{30\pi}{180} = \frac{\pi}{6}.$

$\boxed{\dfrac{\pi}{6}}$ radians

Step 3: Convert $60^\circ$ to radians.

Use the formula
$\theta_radians = \theta_degrees \times \frac{\pi}{180}.$

Substitute $60^\circ$:
$60^\circ \times \frac{\pi}{180} = \frac{60\pi}{180}.$

Simplify the fraction:
$\frac{60\pi}{180} = \frac{\pi}{3}.$

$\boxed{\dfrac{\pi}{3}}$ radians

Step 4: Convert $150^\circ$ to radians.

Use the formula
$\theta_radians = \theta_degrees \times \frac{\pi}{180}.$

Substitute $150^\circ$:
$150^\circ \times \frac{\pi}{180} = \frac{150\pi}{180}.$

Simplify the fraction:
$\frac{150\pi}{180} = \frac{5\pi}{6}.$

$\boxed{\dfrac{5\pi}{6}}$ radians