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zhuklara [117]
3 years ago
11

5+ 3 cos ½x = 7how to find the x?​

Mathematics
1 answer:
Anon25 [30]3 years ago
5 0

Answer:

x=\pm 2 arcos(\frac{2}{3})+4k\pi

where k is an integer

Step-by-step explanation:

5+3\cos(\frac{1}{2}x)=7

We are going to isolate the trig expression first.

Subtract 5 on both sides:

3\cos(\frac{1}{2}x)=2

Divide both sides by 3:

\cos(\frac{1}{2}x)=\frac{2}{3}

Now since \cos(u) is even then \cos(u)=\cos(-u).

So we have:

\cos(\frac{1}{2}x)=\frac{2}{3}

implies:

\frac{1}{2}x=arccos(\frac{2}{3})+2k\pi

Multiply both sides by 2:

x=2arccos(\frac{2}{3})+4k\pi

or

-\frac{1}{2}x=arcos(\frac{2}{3})+2k\pi

Multiply both sides by -2:

x=-2arccos(\frac{2}{3})-4k\pi

So we can say the solution is:

x=\pm 2arcos(\frac{2}{3})+4k\pi

(k is an integer)

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