Math  /  Trigonometry

Question3sin(3xπ)cos(3xπ)=1\sqrt{3} \sin (3 x-\pi)-\cos (3 x-\pi)=1

Studdy Solution
Solve for xx in each case.
Case 1: 3x+π3=π3+2kπ 3x + \frac{\pi}{3} = \frac{\pi}{3} + 2k\pi Subtract π3\frac{\pi}{3} from both sides: 3x=2kπ 3x = 2k\pi Divide by 3: x=2kπ3 x = \frac{2k\pi}{3}
Case 2: 3x+π3=π3+2kπ 3x + \frac{\pi}{3} = -\frac{\pi}{3} + 2k\pi Subtract π3\frac{\pi}{3} from both sides: 3x=2π3+2kπ 3x = -\frac{2\pi}{3} + 2k\pi Divide by 3: x=2π9+2kπ3 x = \frac{-2\pi}{9} + \frac{2k\pi}{3} x=2kπ32π9 x = \frac{2k\pi}{3} - \frac{2\pi}{9}
So the solutions are: x=2kπ3andx=2kπ32π9 x = \frac{2k\pi}{3} \quad \text{and} \quad x = \frac{2k\pi}{3} - \frac{2\pi}{9}
Where kZk \in \mathbb{Z}.

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord