How do you find the exact value of #sin2theta+2sintheta=0# in the interval #0<=theta<360#? Trigonometry Trigonometric Identities and Equations Solving Trigonometric Equations 1 Answer Nityananda Dec 17, 2016 #theta# = 0 and 180 degree Explanation: #sin 2 theta + 2 sin theta = 0# or, # 2sin theta cos theta + 2 sin theta = 0# or, #2 sin theta(cos theta + 1) = 0# or, #2sin theta = 0, (cos theta + 1) = 0# or, #sin theta = 0 and cos theta = -1# or, #theta = o cos theta = cos 180 degree# or, # theta# = 0 and 180 degree [ which is in the interval of # 0<=theta < 360# 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 #\sin^2 x - 2 \sin x - 3 = 0# over the interval #[0,2pi]#? How do you find all the solutions for #2 \sin^2 \frac{x}{4}-3 \cos \frac{x}{4} = 0# over the... How do you solve #\cos^2 x = \frac{1}{16} # over the interval #[0,2pi]#? 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 3565 views around the world You can reuse this answer Creative Commons License