Find the exact value of cosine, start fraction, 4, pi, divided by, 3, end fractioncos 34π​ in simplest form with a rational denominator.Your Answer

The given angle is 4π/3.

Step 1: Convert the angle to a standard position The standard position of an angle is between 0 and 2π. To convert the angle to a standard position, we subtract or add multiples of 2π until the angle is within the range.

4π/3 is already in standard position as it lies between 0 and 2π.

Step 2: Determine the reference angle The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis.

The reference angle for 4π/3 is π/3 because 4π/3 is in the third quadrant and π/3 away from π.

Step 3: Find the cosine of the reference angle The cosine of π/3 is 1/2.

Step 4: Determine the sign of the cosine In the third quadrant, cosine is negative.

So, the cosine of 4π/3 is -1/2.