SOLUTION: (12) Solve for x: sin x = cos (2x + 15) (13) Write an equation that has a root of 3 + i Good morning !! Show work, thanks.

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Question 173168This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: (12) Solve for x: sin x = cos (2x + 15)
(13) Write an equation that has a root of 3 + i
Good morning !! Show work, thanks. This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
12) Solve for x: sin x = cos (2x + 15)
If the sin of an angle = the cos of another angle the angles must be
complementary.
Equation:
x + 2x+15 = 90
3x = 75
x = 25 (one of the angles)
2x+15 = 65 (the other angle)
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(13) Write an equation that has a root of 3 + i
Assuming the coefficients of the resulting equation are all Real Numbers,
if 3+i is a root then 3-i is also a root.
f(x) = (x-(3+i))(x-(3-i))
= ((x-3)-i)((x-3)+i)
= (x-3)^2 - i^2
= x2-6x+9 + 1
= x^2-6x+10
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Cheers,
Stan H.