Find the components of the unit vector that makes an angle of 210 degrees counterclockwise with the positive x-axis

(-√3/2,-1/2)

which would be the same as (cos 210º,sin 210º)

To find the components of the unit vector that makes an angle of 210 degrees counterclockwise with the positive x-axis, we can use the trigonometric functions cosine (cos) and sine (sin).

Step 1: Convert the angle from degrees to radians
Since trigonometric functions in most programming languages and mathematical libraries work with radians, we need to convert the angle from degrees to radians. To convert degrees to radians, we use the formula:

radians = degrees * (π / 180)

In this case, the angle is 210 degrees. So, the conversion would be:

radians = 210 * (π / 180)
= 7π / 6

Step 2: Find the cosine and sine of the angle
The cosine of an angle gives us the x-component of the unit vector, and the sine of an angle gives us the y-component. Using the angle in radians (7π / 6), we can evaluate the cosine and sine using a calculator or mathematical library.

cos(7π / 6) ≈ -√3/2
sin(7π / 6) ≈ -1/2

Therefore, the components of the unit vector that makes an angle of 210 degrees counterclockwise with the positive x-axis are approximately (-√3/2, -1/2).