I have no idea how to solve this problem.
<A is in standard position on a unit circle. Point P (-1/2, -√3/2) is the point of intersection of its terminal side with the unit circle. Find the measure of <A in radians.
Since the angle in in QIII, use the cos=- 1/2 and sin= -sqrt3/2 and the inverse tan function on your calculator since tan is the y/x and is equal to -sqrt3. angle is 60
To find the measure of angle A in radians, we can use the coordinates of point P.
From the given information, we know that point P is at (-1/2, -√3/2), which represents the x and y coordinates respectively.
To find angle A, we need to find the inverse tangent of the y-coordinate divided by the x-coordinate.
This can be represented as:
Θ = arctan(y/x)
Plugging in the values, we have:
Θ = arctan((-√3/2) / (-1/2))
Simplifying further:
Θ = arctan(√3)
Since arctan(√3) is not a special angle value, we can use a calculator to find the approximate value.
Using a calculator, we get:
Θ ≈ 1.047
Therefore, the measure of angle A in radians is approximately 1.047 radians.
To find the measure of angle A in radians, we need to use the coordinates of point P and the unit circle.
First, let's recall that a unit circle is a circle with a radius of 1, centered at the origin (0, 0) in a coordinate plane.
In this problem, we're given the coordinates of point P as (-1/2, -√3/2). Since this point lies on the unit circle, we can use the coordinates to determine the value of the angle.
To find the measure of angle A in radians, we can use the inverse tangent function (tan⁻¹).
The inverse tangent function can be defined as follows:
tan⁻¹(y/x) = θ
Where (x, y) are the coordinates of a point on the unit circle and θ is the measure of the angle in radians.
In our case, the coordinates of point P are (-1/2, -√3/2). Thus, we can substitute these values into the inverse tangent function:
tan⁻¹((-√3/2) / (-1/2))
Now, let's simplify the expression:
tan⁻¹((-√3/2) / (-1/2)) = tan⁻¹(√3)
We know that tan⁻¹(√3) is an angle whose tangent value is √3. Since √3 is a positive value and the tangent is positive in both the first and third quadrants, we can conclude that:
tan⁻¹(√3) = π/3
Therefore, the measure of angle A in radians is π/3.
In summary, to solve the problem, we used the coordinates of point P (-1/2, -√3/2) on the unit circle and the inverse tangent function to find angle A. Finally, we determined that the measure of angle A in radians is π/3.