Question

How do I find the coordinates of 311° on the unit circle?

Answer 1

To find the coordinates of 311° on the unit circle, convert the angle to radians, then calculate the cosine and sine values, keeping in mind the signs associated with the fourth quadrant where this angle is located, resulting in coordinates (cos(311°), -sin(311°)).

Step-by-step explanation:

To find the coordinates of 311° on the unit circle, you can use sine and cosine functions that correspond to the angle. Since a unit circle has a radius of 1, the coordinates at any given angle θ are (cos(θ), sin(θ)). For an angle of 311 degrees, which is almost equivalent to 312 degrees and located in the fourth quadrant, the coordinates can be found as follows:

1. First, convert 311° to radians because trigonometric functions in calculators often require radian measures. There are π radians in 180°, so 311° is (311×π/180) radians.
2. Calculate cos(311°) and sin(311°) using their radian values.
3. The cosine of an angle in the fourth quadrant is positive and the sine is negative. So, cos(311°) will give us the x-coordinate and the negative value of sin(311°) will give us the y-coordinate.

Therefore, the coordinates of 311° on the unit circle will have the form (cos(311°), -sin(311°)).

Answer 2

311 degrees is in the 4th quadrant

the x coordinate is positive while the y coordinate is negative

The radius is one so the x coordinate will be sqrt 1/2 and y cood will be - sqrt (1/2) (using the pythagoras theorem)
as a decimal this will be (0.707, -0.707) to nearest thousanndth