SOLUTION: Hello Tutor, I really need your help to answer this question please. 2. Solve for x: 3 + cos 2x = 7/2; only include answers on [0, 2π]

Algebra ->  Trigonometry-basics -> SOLUTION: Hello Tutor, I really need your help to answer this question please. 2. Solve for x: 3 + cos 2x = 7/2; only include answers on [0, 2π]      Log On


   



Question 971854: Hello Tutor, I really need your help to answer this question please.
2. Solve for x: 3 + cos 2x = 7/2; only include answers on [0, 2π]

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
3+%2B+cos%282x%29%22%22=%22%227%2F2

Clear the fraction by multiplying every term by 2

6+%2B+2cos%282x%29%22%22=%22%227

Subtract 6 from both sides:

2cos%282x%29%22%22=%22%221

Divide both sides by 2

cos%282x%29%22%22=%22%221%2F2

Since 1%2F2 is positive, 2x is in QI or QIV

We want to include all but only all values of x on [0, 2π)
which is the inequality:

0%22%22%3C=%22%22x%22%22%3C%22%222pi

Since our equation involves 2x, not just x, we must multiply 
that inequality through by 2:

0%22%22%3C=%22%222x%22%22%3C%22%224pi

So all possibilities for 2x in that interval for

cos%282x%29%22%22=%22%221%2F2

are



And we solve for x:



Edwn