what is terminal point of 5pi/4?
5pi/4 = pi/4 + pi
So, if you can find the terminal point in QI (pi/4), just change the sign of x and y to put it in QIII.
2,2
To find the terminal point of an angle, you need to use the unit circle.
In this case, the angle is 5π/4.
To find the terminal point, you need to locate the angle on the unit circle.
Start by drawing the unit circle, which is a circle with a radius of 1.
Then, divide the circle into four quadrants.
Since the angle is positive and between π and 2π, it lies in the third quadrant.
From the x-axis, rotate counterclockwise by 5π/4 radians.
This will bring you to the terminal point of the angle.
The terminal point of 5π/4 is (-√2/2, -√2/2).
To find the terminal point of an angle, you can use the unit circle. The terminal point is the point on the unit circle where the angle intercepts the circumference.
The angle 5π/4 is in standard position, which means its initial side coincides with the positive x-axis.
First, let's determine the reference angle. To do that, subtract the nearest multiple of 2π (or 360 degrees) from the given angle:
5π/4 - (4π/4) = π/4
The reference angle is π/4.
Now, let's find the coordinates of the terminal point. Since the reference angle is π/4, we know it falls in Quadrant I. In Quadrant I, the x-coordinate is positive and the y-coordinate is positive.
Using the unit circle, we can determine that the point on the circle that corresponds to the terminal point of π/4 (reference angle) is (√2/2, √2/2).
Therefore, the terminal point of 5π/4 is (√2/2, √2/2).