4 given that θ is a small angle, find an approximation for cos 2θ circle your answer. 1 mark 1 - θ²/2 2…
4 given that θ is a small angle, find an approximation for cos 2θ circle your answer. 1 mark 1 - θ²/2 2 - 2θ² 1 - 2θ² 1 - θ²
Answer
Explanation:
Step1: Recall double - angle formula
$\cos2\theta = 1 - 2\sin^{2}\theta$
Step2: Use small - angle approximation
For small angles $\theta$ (in radians), $\sin\theta\approx\theta$. So, $\sin^{2}\theta\approx\theta^{2}$.
Step3: Substitute small - angle approximation
Substitute $\sin^{2}\theta\approx\theta^{2}$ into the double - angle formula: $\cos2\theta\approx1 - 2\theta^{2}$
Answer:
$1 - 2\theta^{2}$