The point P (-7.00, -2.00) is on the terminal arm of an angle in standard position.
Determine the measure of the principal angle to the nearest tenth of radians.
Enter the numerical value in the space below.
it is QIII, and tanθ = -2/-7
so θ = π + 0.278
To find the measure of the principal angle, we need to determine the angle formed by the point P (-7.00, -2.00) on the coordinate plane in standard position.
First, let's find the distance from the origin (0, 0) to the point P (-7.00, -2.00) using the distance formula:
distance = √[(x2 - x1)² + (y2 - y1)²]
distance = √[(0 - (-7.00))² + (0 - (-2.00))²]
distance = √[(7.00)² + (2.00)²]
distance = √[49.00 + 4.00]
distance = √53.00
distance ≈ 7.28
Next, we find the angle formed by the point P in standard position by using the inverse tangent function:
angle = arctan(y / x)
angle = arctan((-2.00) / (-7.00))
angle ≈ arctan(0.2857)
angle ≈ 0.2843 radians (rounded to the nearest tenth)
Therefore, the measure of the principal angle to the nearest tenth of a radian for point P (-7.00, -2.00) is approximately 0.3 radians.