Question

Solve, finding all solutions in [0,2π)
-cos(π-x)-sin(x-π/2)=-1

Answer 1

Answer on Question#41693 – Math - Trigonometry

Question:

Solve, finding all solutions in [0,2π)

- cos(π-x)-sin(x-π/2)=-1

Solution:

1) - cos(π - x) - sin\left(x - \frac{\pi}{2}\right) = -1

2) $\cos(x) + \sin\left(\frac{\pi}{2} - x\right) = -1$

3) $\cos(x) + \cos(x) = -1$

4) $\cos(x) = -\frac{1}{2}$

5) $x = \frac{2\pi}{3} \text{ or } x = \frac{4\pi}{3}$

Answer: $x = \frac{2\pi}{3}$ or $x = \frac{4\pi}{3}$

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