SOLUTION: Find, to the nearest degree, all values of x in the interval 0° ≤ x ≤ 360° that satisfy the equation 3 cos 2x + cos x + 2 = 0. Please check my answers to see if I a

Algebra.Com
Question 389120: Find, to the nearest degree, all values of x in the interval 0° ≤ x ≤ 360° that satisfy the equation 3 cos 2x + cos x + 2 = 0.
Please check my answers to see if I am correct: 71°; 60°; 300° and 289°
Thanks
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
You got two right and two wrong!



Use the identity  







Factor the left side:



Use the zero-factor principle for the first factor:







We find the inverse cosine of  as 70.52877937°, which is
the reference angle.

Rounded to the nearest degree is 71°.  Since  is a positive
number and the Cosine is positive in the 1st and 4th quadrants, the
solutions are 71° for the 1st quadrant solution (same as the reference
angle) and 360°-70.52877937° = 289.4712206 or 289° for the 4th quadrant 
solution.




Use the zero-factor principle for the second factor:







We find the inverse cosine of  as 60°, the reference
angle.

Since  is a negative number and the Cosine is negative
in the 2nd and 3rd quadrants, the solutions are 180°-60° = 120° 
for the 2nd quadrant solution and 180°+60° = 240° for the 3rd quadrant
solution.

So the four correct answers to the nearest degree are:

71°, 289°, 120°, 240°

Edwin
RELATED QUESTIONS

Find, to the nearest degree, all values of x in the interval 0° ≤ x ≤ 360°... (answered by Fombitz)
Find all values of θ in the interval 0 ≤ θ≤ 360•that satisfy the... (answered by lwsshak3)
Find to the nearest degree, all values of X in the interval 0°≤X≤360° which... (answered by lwsshak3)
find to the nearest degree, all values of x between 0 degrees and 360 degrees that... (answered by robertb)
1)Find all real numbers that satisfy the equation: cos x = square root 3 / 2. 2)Solve... (answered by lynnlo)
To the nearest degree, the values of x in the interval 0° ≤ x < 360° that satisfy... (answered by KMST)
Find the values of x in the interval 0° ≤ x ≤ 360° for which sin(x) =... (answered by lwsshak3)
Find all values of θ, to the nearest degree, that satisfy the equation 7cos... (answered by lwsshak3)
Find all values of x in the interval 0 degreesis less than or equal to x wich is less... (answered by jsmallt9)