Solve \cos \left(\frac{\pi }{3}-2x\right)-1=-\frac{1}

Evaluate

cos (\frac{π}{3} - 2 x) - 1 = - \frac{1}{2}

Move the constant to the right-hand side and change its sign

cos (\frac{π}{3} - 2 x) = - \frac{1}{2} + 1

Add the numbers

More Steps

cos (\frac{π}{3} - 2 x) = \frac{1}{2}

Use the inverse trigonometric function

\frac{π}{3} - 2 x = arccos (\frac{1}{2})

Calculate

\frac{π}{3} - 2 x = \frac{π}{3} \frac{π}{3} - 2 x = \frac{5 π}{3}

Add the period of 2 kπ, k \in Z to find all solutions

\frac{π}{3} - 2 x = \frac{π}{3} + 2 kπ, k \in Z \frac{π}{3} - 2 x = \frac{5 π}{3} + 2 kπ, k \in Z

Calculate

More Steps

x = kπ, k \in Z \frac{π}{3} - 2 x = \frac{5 π}{3} + 2 kπ, k \in Z

Calculate

More Steps

x = kπ, k \in Z x = \frac{π}{3} + kπ, k \in Z

Solution

x = {kπ \frac{π}{3} + kπ, k \in Z

Alternative Form

x = {18 0^{\circ} k 6 0^{\circ} + 18 0^{\circ} k, k \in Z

Alternative Form

x \approx {kπ 1.047198 + kπ, k \in Z

Solve the equation