Find the value of theta (in radians) corresponding to the point (6,-8)
To find the value of theta corresponding to the point (6,-8), we can use trigonometry. The angle theta is the angle between the positive x-axis and the line connecting the origin to the point (6,-8).
Step 1: Find the length of the line connecting the origin to the point (6,-8) using the Pythagorean theorem.
The length of the line is equal to the square root of the sum of the squares of the x-coordinate and the y-coordinate:
length = sqrt(6^2 + (-8)^2) = sqrt(36 + 64) = sqrt(100) = 10.
Step 2: Use the inverse tangent function to find the angle theta.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is -8 (the y-coordinate) and the adjacent side is 6 (the x-coordinate). Therefore, the tangent of theta is -8/6 = -4/3.
Now, we can use the inverse tangent function (also known as the arctangent function) to find theta:
theta = arctan(-4/3).
Using a calculator or a math software, you can find the value of arctan(-4/3) is approximately -0.93 radians or -53.13 degrees.
So, the value of theta, in radians, corresponding to the point (6,-8) is approximately -0.93 radians.