Choose the point on the terminal side of 135°
To choose the point on the terminal side of 135°, we need to visualize a coordinate plane and understand the unit circle.
1. Start by drawing a coordinate plane, with the x-axis horizontal (positive to the right) and the y-axis vertical (positive upwards).
2. Next, draw a circle with its center at the origin (0,0) and a radius of 1 unit. This circle is called the unit circle.
3. Now, locate the initial side of the angle. Since the angle is measured counterclockwise from the positive x-axis, the initial side starts at the positive x-axis.
4. Starting from the initial side, rotate counterclockwise by 135 degrees. This will bring you to the terminal side of the angle.
5. At 135 degrees, the terminal side of the angle will intersect the unit circle at a certain point. To find this point, we must determine the coordinates of the intersection.
6. Since the point is on the unit circle, the distance from the origin to the point is 1 unit. This means that the coordinates of the point (x, y) represent the ratios of the lengths of the legs of a right triangle formed by the point, the x-axis, and a line extending from the origin to the point.
7. To calculate the coordinates, we can use trigonometric ratios. In this case, the angle is 135 degrees, or π/4 radians. The trigonometric ratios for this angle are sin(π/4) and cos(π/4).
8. The coordinates of the point on the terminal side of 135 degrees are (cos(π/4), sin(π/4)). Evaluating these trigonometric ratios, we get approximately (0.707, 0.707).
So, the point on the terminal side of 135 degrees is approximately (0.707, 0.707).
To choose the point on the terminal side of 135° in the Cartesian coordinate system, follow these steps:
1. Start at the origin (0, 0).
2. Draw a line from the origin that makes an angle of 135° with the positive x-axis, in the counterclockwise direction.
3. Measure the distance along this line from the origin. This will be the distance from the origin to the point on the terminal side of 135°.
4. Mark the point where the line intersects the circle with radius equal to the distance measured in the previous step, centered at the origin. This will be the point on the terminal side of 135°.
Note: The coordinates of this point will depend on the radius of the circle or the measured distance from the origin.