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compute the smallest positive real solution to the equation sin(7x) = cos (3x − π/14) + 2.

 

 

Hints/starting ideas would be appreciated. 

 Jun 19, 2021
 #1
avatar+287 
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Well, will it help to know that the desired smallest positive x is in the interval (1.1, 1.2)?

 Jun 20, 2021
 #2
avatar+2250 
+1

sin(7x) = cos (3x − π/14) + 2

cos(7x - pi/2) = cos(3x − π/14) + 2

 

Note that cos(a) has to return a number from -1, to 1. 

So the only way this equation is possible is if cos(3x − π/14) = -1 and cos(7x - pi/2) = 1. 

cos(3x − π/14) = -1

cos(7x - pi/2) = 1

Can you take it from here?

=^._.^=

 Jun 20, 2021

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