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Submission: On May 19 via manual from CA — Scanned from CA
Effective URL: https://socratic.org/questions/how-do-you-find-all-values-of-x-such-that-sin-2x-sin-x-and-0-x-2pi
Submission: On May 19 via manual from CA — Scanned from CA
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* Trigonometry SCIENCE * Anatomy & Physiology * Astronomy * Astrophysics * Biology * Chemistry * Earth Science * Environmental Science * Organic Chemistry * Physics MATH * Algebra * Calculus * Geometry * Prealgebra * Precalculus * Statistics * Trigonometry HUMANITIES * English Grammar * U.S. History * World History ... AND BEYOND * Socratic Meta * Featured Answers Topics HOW DO YOU FIND ALL VALUES OF X SUCH THAT SIN2X=SINX AND 0≤X≤2Π? Trigonometry Trigonometric Identities and Equations Solving Trigonometric Equations 1 ANSWER Shwetank Mauria May 22, 2016 x=nπ or x=2nπ±π3 EXPLANATION: As sin2x=sinx, we have 2sinxcosx=sinx or 2sinxcosx−sinx=0 sinx(2cosx−1)=0 i.e. either sinx=0 which implies x=nπ or 2cosx−1=0 i.e. cosx=12=cos(±π3) which implies x=2nπ±π3 Answer link RELATED QUESTIONS * How do you find all solutions trigonometric equations? * How do you express trigonometric expressions in simplest form? * How do you solve trigonometric equations by factoring? * How do you solve trigonometric equations by the quadratic formula? * How do you use the fundamental identities to solve trigonometric equations? * What are other methods for solving equations that can be adapted to solving trigonometric equations? * How do you solve sin2x−2sinx−3=0 over the interval [0,2π]? * How do you find all the solutions for 2sin2x4−3cosx4=0 over the... * How do you solve cos2x=116 over the interval [0,2π]? * How do you solve for x in 3sin2x=cos2x for the interval 0≤x<2π See all questions in Solving Trigonometric Equations IMPACT OF THIS QUESTION 38249 views around the world You can reuse this answer Creative Commons License * iOS * Android * Privacy * Terms * Help