Question

Point A is on the terminal side of theta where θ=3/8π. What is the coordinate of this point on the unit circle? Round to the hundredths place.

a) (0.38, 0.92)
b) (0.71, 0.71)
c) (0.92, 0.38)
d) (0.29, 0.96)

Answer 1

The coordinate of point A on the unit circle at θ=3/8π is approximately (0.71, 0.71), which is answer option b). To find this, the cosine and sine functions are used to calculate the x and y coordinates respectively.

Step-by-step explanation:

The task is to find the coordinates of point A on the unit circle at an angle of θ=3/8π. Since the unit circle has a radius of 1, we can use the sine and cosine functions to find the coordinates of any point on the circle. The x-coordinate is equal to cos(θ) and the y-coordinate is equal to sin(θ), where θ is the angle from the positive x-axis to the point, moving counter-clockwise. For θ=3/8π: θ in radians is 3/8 times π which is approximately 1.1781 radians. The x-coordinate is cos(3/8π) which is approximately 0.71 (rounded to the hundredth place). The y-coordinate is sin(3/8π) which is also approximately 0.71 (rounded to the hundredth place). Thus, the coordinate of point A on the unit circle is approximately (0.71, 0.71), which matches option b).