Let O represent the origin and P be the point (9, -4). Find the positive angle (counterclock wise direction)that the line segment OP makes with the positive x-axis.
the answer is 5.86 radians but i keep getting 0.418 radian. please help and show work
Isn't your angle in the fourth quadrant?
Your angle in standard position (the corresponding angle if the triangle had been in the first quadrant is inversetan(4/9) which is .418
so your angle in the 4th quadrant is 2pi - .418 = 5.865
To find the positive angle that the line segment OP makes with the positive x-axis, you can use trigonometry. Let's go through the steps to calculate it correctly.
Step 1: Determine the coordinates of point P.
Given that point P is located at (9, -4).
Step 2: Calculate the length of line segment OP.
Using the distance formula, the length of line segment OP can be found:
OP = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((9 - 0)^2 + (-4 - 0)^2)
= sqrt(9^2 + (-4)^2)
= sqrt(81 + 16)
= sqrt(97)
Therefore, OP = sqrt(97).
Step 3: Determine the angle θ with the positive x-axis.
The angle θ can be found using the formula:
θ = arctan(y/x)
In this case, y = -4 and x = 9.
θ = arctan(-4/9)
Arctan(-4/9) is approximately -0.418 radians.
However, we want to find the positive angle in the counterclockwise direction, so we need to add a full revolution of 2π radians (approximately 6.28 radians).
θ = -0.418 + 2π
≈ 5.86 radians
Therefore, the positive angle that the line segment OP makes with the positive x-axis is approximately 5.86 radians.