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

To convert degrees to radians, use the formula

$$\theta_\text{radians} = \theta_\text{degrees} \times \frac{\pi}{180}.$$

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

Use the formula

$$\theta_\text{radians} = \theta_\text{degrees} \times \frac{\pi}{180}.$$

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

Use the formula

$$\theta_\text{radians} = \theta_\text{degrees} \times \frac{\pi}{180}.$$

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

Use the formula

$$\theta_\text{radians} = \theta_\text{degrees} \times \frac{\pi}{180}.$$

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