Final answer:
The trigonometric equation 2cos(θ) - √3 = 0 is factored by isolating cos(θ) to find cos(θ) = √3/2. The angles that satisfy this equation are typically 30° or 330° in standard position, but the general solution includes adding multiples of 360° to these angles for all possible solutions.
Step-by-step explanation:
We are asked to factor the trigonometric equation 2cos(θ) - √3 = 0. To solve this, we need to isolate cos(θ) by adding √3 to both sides of the equation, which gives us 2cos(θ) = √3. Next, divide both sides by 2 to obtain cos(θ) = √3/2. This equation suggests that the angle θ has a cosine of √3/2, which are specific angles on the unit circle.
Those angles where the cosine is √3/2 are typically 30° or 330° in standard position, but when considering all possible solutions, we would write the general solution as θ = 30° + 360°k and θ = 330° + 360°k where k is any integer.
To factor the equation 2cos(θ) - √3 = 0, we can first isolate the cosine term by adding √3 to both sides of the equation:
2cos(θ) = √3
Then, divide both sides by 2:
cos(θ) = √3/2
The equation cos(θ) = √3/2 has two solutions, which correspond to the angles where the cosine function is equal to √3/2. These angles are π/6 and -π/6. So the solutions for θ are π/6 and -π/6.