Question

Where do the graphs of f(x)=cos(x/2) and g(x)= sqrt2 - cos(x/2) intersect on the interval [0,360)?

(See image below for clear question and answer choices)

Answer 1

(a) 90°

Explanation:

A graph can help you answer the question about where the graphs of the two functions intersect. It shows the one angle of intersection to be 90°.

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You can also determine this analytically.

f(x) = g(x)

cos(x/2) = √2 -cos(x/2)

2cos(x/2) = √2 . . . . . . . . . . add cos(x/2)

cos(x/2) = √2/2 . . . . . . . . divide by 2

x/2 = ±45° +360°×n . . . . . for an integer n

x = ±90 +720°×n . . . . multiply by 2

x = 90° is the only solution in the desired range.