If 2cos A-1=0 where 0<or = A<2pi then what is A equal to?
2cosA = 1
cosA = 1/2
A = π/3 (60 degrees) or A = 5π/3 (300 degrees)
the answer is 60 degrees
To find the value of A when 2cos A - 1 = 0, we need to isolate the variable A.
Step 1: Add 1 to both sides of the equation to get rid of the -1:
2cos A - 1 + 1 = 0 + 1
2cos A = 1
Step 2: Divide both sides of the equation by 2 to solve for cos A:
2cos A / 2 = 1 / 2
cos A = 1/2
Now, to determine the value of A within the given range (0 ≤ A < 2π) where cos A = 1/2, we can use the inverse cosine function (also known as arc cosine or cos^(-1)).
Step 3: Take the inverse cosine of both sides of the equation:
A = cos^(-1)(1/2)
The inverse cosine of 1/2 is π/3 or 60 degrees. However, since the given range is 0 ≤ A < 2π, we need to find the other possible solutions within this range.
Step 4: Since the cosine function has a repeating pattern, we can find additional solutions by adding or subtracting multiples of the period of cos A, which is 2π.
In this case, the inverse cosine of 1/2 is π/3, which is within the given range (0 ≤ A < 2π), so A = π/3 is a valid solution.
To find the additional solutions, we add or subtract multiples of 2π from π/3:
A = π/3 + 2π or A = π/3 - 2π
Simplifying these expressions, we have:
A = π/3, A = π/3 + 6π, and A = π/3 - 6π
Since the given range is from 0 to 2π, the values A = π/3 + 6π and A = π/3 - 6π fall outside of this range, so they are not valid solutions.
Therefore, the value of A within the given range 0 ≤ A < 2π when 2cos A - 1 = 0 is A = π/3.