SOLUTION: Given sinθ, 2 cosθ and 2 sinθ are three consecutive terms in an arithmetic sequence. Find the value of θ in radians given θ is an acute angle.

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Question 1111789: Given sinθ, 2 cosθ and 2 sinθ are three consecutive terms in an arithmetic sequence. Find the value of θ in radians given θ is an acute angle.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Given three consecutive terms in an arithmetic sequence, the middle one is the average of the other two. So in this problem
2cos%28x%29+=+%28sin%28x%29%2B2sin%28x%29%29%2F2
4cos%28x%29+=+3sin%28x%29
sin%28x%29%2Fcos%28x%29+=+4%2F3
tan%28x%29+=+4%2F3
x = arctan(4/3)