Given theta is in the standard position and is in the first quadrant , if the terminal side of the angle theta is parallel to the line y=x+4 on ,find the measure of theta in degrees.
slope is 1 on the line, so tanTheta=1
theta=arctan1=45 degrees
Thank you!
To find the measure of theta in degrees, we can use the slope of the line y=x+4.
In the first quadrant, the terminal side of the angle is parallel to the line y=x+4. This means that the slope of the line is equal to the tangent of the angle.
The slope of a line in the form y=mx+b is represented by the value of m. In this case, the slope is 1.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle. In this case, the length of the side opposite the angle is 1 and the length of the side adjacent to the angle is 4.
Therefore, the tangent of theta is 1/4.
To find the measure of theta, we can use the inverse tangent function (also known as arctan or tan^(-1)). Taking the inverse tangent of 1/4 will give us the angle in radians.
arctan(1/4) ≈ 0.2449786631 radians
To convert the angle from radians to degrees, we can use the fact that there are 180 degrees in π radians.
0.2449786631 radians ≈ 14.0362434675 degrees
Therefore, the measure of theta is approximately 14.04 degrees.