IB Maths AA 3.4 Notes

Radians

A radian is another unit for measuring angles. The key conversion is:

$\pi\text{ radians}=180^\circ$

So to convert:

• from degrees to radians, multiply by $\frac{\pi}{180}$
• from radians to degrees, multiply by $\frac{180}{\pi}$

Write $45^\circ$ in radians.

$45\times\frac{\pi}{180}=\frac{\pi}{4}$.

So $45^\circ=\frac{\pi}{4}$.

Write $\frac{2\pi}{3}$ radians in degrees.

$\frac{2\pi}{3}\times\frac{180}{\pi}=120$.

So $\frac{2\pi}{3}=120^\circ$.

Some common exact angles you will need to memorise are:

• $30^\circ=\frac{\pi}{6}$
• $45^\circ=\frac{\pi}{4}$
• $60^\circ=\frac{\pi}{3}$
• $90^\circ=\frac{\pi}{2}$
• $180^\circ=\pi$
• $360^\circ=2\pi$

As you will see, radians are a more natural way of defining angles and allow geometric formulas to be simplified.

Make sure the calculator is in the correct angle mode when working with trigonometric functions. This will matter for circle formulas and trig functions that appear elsewhere.