For what value of x does 6 sin (2x - 25)o attain its maximum value in the range 0o \(\leq\) x \(\leq\) 180o
A
12\(\frac{1}{2}\)
B
32\(\frac{1}{2}\)
C
57\(\frac{1}{2}\)
D
147\(\frac{1}{2}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
y = 6 sin (2x - 25)º
\(\frac{dy}{dx}\) = 12 cos(2x - 25)º
\(\frac{dy}{dx}\) = 0
12 cos x (2x - 25º) = 0
= cos(2x - 25º) = 0
= 2x - 25º = cos\(^{-1}\)(0)
= 2x - 25º = 90º
x = \(\frac{115}{2}\)
Source: Myschool Past Questions Archive (Record #30759)