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
Try checking your graph. Accuracy when graphing a coordinate is vital.
To find the angle that the line segment OP makes with the positive x-axis, we can use the arctangent function.
First, let's find the slope of the line segment OP. Slope is defined as the change in y divided by the change in x.
Change in y = -4 - 0 = -4
Change in x = 9 - 0 = 9
Slope = change in y / change in x
= -4 / 9
Next, we can use the arctangent function to find the angle. The arctangent of a slope gives us the angle it makes with the positive x-axis.
Angle = arctan(slope)
= arctan(-4/9)
Using a calculator or a tool with trigonometric functions, we can calculate the arctan value to find the angle.
Angle ≈ -0.418 radians (approximately -0.418)
It seems you were getting -0.418 radians as your answer. However, the question asks for the counterclockwise angle, which should be positive. In order to get the positive angle, we can add a full revolution of 2π to the negative result.
Positive angle = -0.418 + 2π
Since 2π is approximately 6.283, we have:
Positive angle ≈ -0.418 + 6.283
= 5.865 radians (approximately 5.865)
So the correct answer is approximately 5.865 radians, which is the positive angle that the line segment OP makes with the positive x-axis.