Question

Consider the function f(x) = sin(x + pi/3) + sin(x - pi/3) over the interval [0, 2pi). Simplify the formula of this function and find its maximum value on this interval. a) sqrt(3)/2 b) 1 c) 1/2 d) sqrt(2) e) sqrt(3) f) None of the above.

          Consider the function f(x) = sin(x + pi/3) + sin(x - pi/3) over the interval [0, 2pi). Simplify the formula of this function and find its maximum value on this interval.

a) sqrt(3)/2
b) 1
c) 1/2
d) sqrt(2)
e) sqrt(3)
f) None of the above.

Consider the function f(x) = sin(x + pi/3) + sin(x - pi/3) over the interval [0, 2pi). Simplify the formula of this function and find its maximum value on this interval.

a) sqrt(3)/2
b) 1
c) 1/2
d) sqrt(2)
e) sqrt(3)
f) None of the above.

Added by Heidi E.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Gregory Higby

12/31/2021

Step 1

Step 1:** Apply the sum and difference formulas for sine to simplify the expression: \[ f(z) = \sqrt{e^x} + i \sin(x + \frac{\pi}{3}) \] Using the sum formula for sine: \[ \sin(a + b) = \sin(a)\cos(b) + \cos(a)\sin(b) \] We have: \[ \sin(x + \frac{\pi}{3}) = Show more…

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Consider the function f(x) = sin(x + pi/3) + sin(x - pi/3) over the interval [0, 2pi). Simplify the formula of this function and find its maximum value on this interval.