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# find the solution algebraically for cos 2x+2 = sin x

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find the solution algebraically for cos 2x+2 = sin x

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#1
+4728
+1

Since sin x can't be bigger than 1, assuming this is the question

cos (2x + 2) = sin x

*edit* That was a bad thing to assume!

This is probably not the answer you want.. see CPhill's answer vvvv

But if you did happen to mean that:

This is to make it easier to see that

x + (2x + 2) = 90

x + 2x + 2 = 90

3x = 88

x = 88/3

hectictar  Apr 13, 2017
edited by hectictar  Apr 13, 2017
edited by hectictar  Apr 13, 2017
#2
+76976
+2

cos 2x + 2 = sin x

1 - 2sin^2x + 2  = sinx

2sin^2x  + sinx - 3   =  0

(2sin x  + 3) ( sin x - 1)  =  0

The first factor has no solution

For the second, we have

sin x  - 1   = 0

sin x  =  1         and this happens at pi/2  + 2pi*n    where n is an integer

See the graph here showing the intersection points  :

https://www.desmos.com/calculator/31maw6isd8

CPhill  Apr 13, 2017

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