SOLUTION: This is a Trigonometry and quadratic question but I couldn't find that as a topic. find all solutions, if possible, of the below equation on the interval [0, 2pi]: sin^2x + 3 c

Algebra ->  Trigonometry-basics -> SOLUTION: This is a Trigonometry and quadratic question but I couldn't find that as a topic. find all solutions, if possible, of the below equation on the interval [0, 2pi]: sin^2x + 3 c      Log On


   

Question 687890: This is a Trigonometry and quadratic question but I couldn't find that as a topic.
find all solutions, if possible, of the below equation on the interval [0, 2pi]: sin^2x + 3 cos^2 x =0

also, the given answer is "No solution".
Thank you in advance I need to show my whole class how to do this on Monday, and I'm worried I wont get it right.
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the identity sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1


Using the identity sin%5E2%28x%29+%2B+3+cos%5E2%28x%29+=0 becomes sin%5E2%28x%29%2B3%2A%281-sin%5E2%28x%29%29+=+0--->sin%5E2%28x%29%2B3+-+3%2Asin%5E2%28x%29=0--->-2%2Asin%5E2%28x%29%2B3+=0--->3=2sin%5E2%28x%29 --->3%2F2+=+sin%5E2%28x%29


Take the square root of both sides.


sqrt%283%2F2%29+=+sin%28x%29+=+1.225 or sin%28x%29+=+-1.225


That can't be true because sin(x) never exceeds 1 or falls below -1. So the answer is no solution.

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