Radian Help

Have to complete this for the end of this month but I've never been taught it? Any help would be appreciated, sorry if the photo is turned around

Have to complete this for the end of this month but I've never been taught it? Any help would be appreciated, sorry if the photo is turned around

As stated, radians are an alternate way of measuring angles, and soon enough throughout A-level maths you will realise that it is the better way. Angles are measured in terms of $\pi$ when in radians. You need to know that $180 \text{degrees}=\pi \text{radians}$, therefore $90 \text{degress} = \frac{\pi}{2}\text{radians} , 360 \text{degrees}=2\pi \text{radians}$ and so on.

To convert an angle of $n$ degrees into radians, you take that number and multiply it by $\frac{\pi}{180}$ (you can see that the fraction would equal 1 as the numerator is the same as denominator, just in different measurements, so the quantity remains unchanged). This would gives you $\theta=\frac{n\pi}{180}$ where $\theta$ is the angle in radians.

To convert an angle of $m$ radians into degrees, you take that number and multiply it by $\frac{180}{\pi}$ (the reciprocal of the first one). This gives you $\phi = \frac{180m}{\pi}$ where $\phi$ is the angle in degrees.

Radians are useful in calculating arc length and area of sectors and such, especially for circles with these simple formulae:
$A_{rc}=r\theta$
$A_{rea}=\frac{1}{2}r^2\theta$
...where $r$ is the radius of the circle.

It will also become necessary to use them when integrating trig functions. Other than that I'm not sure what else to tell ya.

A radian is the angle subtended when the arc length is equal to the radius. There are $2\pi$ radii in the circumference of a circle, so there are $2\pi$ radians in a full circle.
Everything thing else follows from this.

Much better to use tau as then e.g. tau/4 radians is a quarter circle, tau/3 is a third of a circle, etc., whereas e.g. pi/2 not being a half circle makes no sense. For more information see http://tauday.com/tau-manifesto

Much better to use tau as then e.g. tau/4 radians is a quarter circle, tau/3 is a third of a circle, etc., whereas e.g. pi/2 not being a half circle makes no sense. For more information see http://tauday.com/tau-manifesto

I'm not a fan of $\tau$ and in schools it's only ever $\pi$ that is mentioned.