cos(x) = sin(x - 1) - Math Central

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Question from alex, a student:

hi
i have a problem:
in the equation cos x = sin x-1 for -pi/2 <x <pi/2
A: solve for x graphically
B: solve algebraically and prove the solution is correct.
part A is easy enough, ploy y=cos x and y= sin = x-1
and the point that the 2 waves intersect is (1.28,0.28)
the problem is trying to solve this algebraically,
according to my understanding sin x-1 is the same as cos x, so how can i get the value
x= 1.28

any help much appreciated
cheers
Alex

Alex,

You have cos(x) = sin(x - 1). Use the multiple angle expression for the sine function

sin (A + B) = sin(A) cos(B) + cos(A) sin(B)

to expand the right side and simplify to obtain an expression of the form tan(x) = "some expression involving sin(1) and cos(1)". Use your calculator to evaluate the right side and then use the inverse tangent function to find x.

I hope this helps,
Penny

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