I assume you're asked to solve
4 cos²(<em>x</em>) - 7 cos(<em>x</em>) + 3 = 0
Factor the left side:
(4 cos(<em>x</em>) - 3) (cos(<em>x</em>) - 1) = 0
Then either
4 cos(<em>x</em>) - 3 = 0 <u>or</u> cos(<em>x</em>) - 1 = 0
cos(<em>x</em>) = 3/4 <u>or</u> cos(<em>x</em>) = 1
From the first case, we get
<em>x</em> = cos⁻¹(3/4) + 2<em>nπ</em> <u>or</u> <em>x</em> = -cos⁻¹(3/4) + 2<em>nπ</em>
and from the second,
<em>x</em> = <em>nπ</em>
where <em>n</em> is any integer.
Answer: the coordinates of B' are (6, -13)
Justification:
1) Translating triangle ABC according to the rule (x,y) → (x + 2, y - 8) means that every single point of the triangle will be translated two units to the righ (x + 2) and 8 units downward (y - 8).
2) To find the coordinates of anay image you have to add up 2 to the x coordinate (x + 2) and subtract 8 from the y-coordinate (y - 8).
3) Peforming those simple operations to the coordinates of the point B (4, -5), you will obtain the point B':
* x' = x + 2 = 4 + 2 = 6
* y' = y - 8 = -5 - 8 = - 13
Answer: the coordinates of B' are (6, -13)
