Question 1195724: Given that sin(5x-28) = cos(3x-50), find the value of x.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sin(theta) = cos(90 - theta)
you get:
theta = 5x - 28
90 - theta = 3x - 50
solve for theta in the second equation to get:
theta = 90 - 3x + 50
since they both = theta, this gets you:
5x - 28 = 90 - 3x + 50
add 3x to both sides of the equation and add 28 to both sides of the equation to get:
8x = 90 + 28 + 50 = 168
solve for x to get:
x = 168/8 = 21.
sin(5x - 28) becomes sin(77)
cos(3x - 50) becomes cos(13)
sin(77) = .9743700648
cos(13) = .9843700648
they're the same, confirming that x = 21 is your answer.
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