Question

Solve on the interval [0/2pi] 1-cos(theta) = (1/2)

Answer 1

Answer:

Final answer is $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$.

Step-by-step explanation:

Given equation is $1-\cos\left(\theta\right)=\frac{1}{2}$

Now we need to find the solution of  $1-\cos\left(\theta\right)=\frac{1}{2}$ in given interval $[0, 2\pi ]$.

$1-\cos\left(\theta\right)=\frac{1}{2}$

$-\cos\left(\theta\right)=\frac{1}{2}-1$

$-\cos\left(\theta\right)=-\frac{1}{2}$

$\cos\left(\theta\right)=\frac{1}{2}$

which gives $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$ in the given interval.

Hence final answer is $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$.