Radians questions with answers

Questions

1. Question 1Degrees to radians, in terms of π

   Express $36^\circ$ in radians, in terms of $\pi$.

   Show the worked solution

   1. Step 1: π radians = 180°To change degrees to radians, multiply by $\dfrac{\pi}{180}$.
   2. Step 2: Multiply and simplify the fraction$\mathstrut 36^\circ = 36 \times \dfrac{\pi}{180}$$36^\circ = \dfrac{\pi}{5}$
2. Question 2Degrees to radians, to 3 s.f.

   Express $143^\circ$ in radians, correct to 3 significant figures.

   Show the worked solution

   1. Step 1: π radians = 180°To change degrees to radians, multiply by $\dfrac{\pi}{180}$.
   2. Step 2: Multiply, then round$\mathstrut 143^\circ = 143 \times \dfrac{\pi}{180}$$143^\circ = 2.4958\ldots$$143^\circ = 2.50$ rad (3 s.f.)
3. Question 3Radians in terms of π to degrees

   Express $\dfrac{\pi}{4}$ radians in degrees.

   Show the worked solution

   1. Step 1: Write it in degrees$\mathstrut \dfrac{\pi}{4} = \dfrac{180^\circ}{4}$
   2. Step 2: Work it out$\dfrac{\pi}{4} = 45^\circ$
4. Question 4Radians to degrees, to 1 d.p.

   Express $2.95$ radians in degrees, correct to 1 decimal place.

   Show the worked solution

   1. Step 1: π radians = 180°To change radians to degrees, multiply by $\dfrac{180}{\pi}$.
   2. Step 2: Multiply, then round$\mathstrut 2.95 \text{ rad} = 2.95 \times \dfrac{180}{\pi}$$2.95 \text{ rad} = 169.0225\ldots^\circ$$2.95 \text{ rad} = 169.0^\circ$ (1 d.p.)