Final answer:
The terminal points on the unit circle for given angles are based on the cosine and sine functions. Terminal points for π/4 and 3π/4 lie in the first and second quadrants respectively, with corresponding signs, while -π/4 and -3π/4 lie in the fourth and third quadrants.
Step-by-step explanation:
-3π/4 The question pertains to finding the terminal point of angles on the unit circle. For angles π/4, -π/4, 3π/4, and -3π/4, we determine the coordinates using the standard unit circle where the radius (r) is 1. Since these angles are in relation to the x-axis, the terminal points are:π/4: The terminal point is at (sqrt(2)/2, sqrt(2)/2).-π/4: This is the reflection of π/4 across the x-axis, so the point is (sqrt(2)/2, -sqrt(2)/2)3π/4: The point is opposite to π/4 on the unit circle, yielding (-sqrt(2)/2, sqrt(2)/2)-3π/4:
This is also opposite to π/4 but below the x-axis, so the terminal point is (-sqrt(2)/2, -sqrt(2)/2).Each angle results in a unique terminal point on the circle, with their values being based on the sine and cosine of the respective angles.The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. The terminal point of an angle on the unit circle is the point where the angle intersects the circle. To find the terminal point for each angle given (π/4, -π/4, 3π/4, -3π/4), we can use the coordinates provided. For example, for angle π/4, the terminal point is (0, 1) since the coordinates given are (0, 0, -0.866, -17.32).