Small angle approximationsEdexcel A-Level Maths: Mind map

Exam questions on Small angle approximations

1. In this question $\theta$ is small and measured in radians, so the standard small angle approximations may be used.
   Calculate the percentage error in the estimate $\cos0.2\approx0.98$, using the calculator value of $\cos0.2$. Give your answer to 2 significant figures.2 marks
2. For small $x$ in radians, consider the expression $E=\frac{1-\cos4x}{x\tan2x}$.
   Hence find the approximate value of $E$ when $x$ is small.2 marks
3. A pendulum of length $1.5$ m swings through a small angle $\theta$ radians from the vertical. The horizontal displacement of the bob from the vertical is $d=1.5\sin\theta$ m and its height above its lowest point is $h=1.5(1-\cos\theta)$ m.
   Use a small angle approximation to show that, for small $\theta$, $h\approx0.75\theta^2$.3 marks