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Answer 1 To find the coordinates of the point on the unit circle where the angle is $\frac{3\pi}{4}$ radians, we use the unit circle definition:The coordinates are given by:$ (\cos\theta, \sin\theta) $For $ \theta = \frac{3\pi}{4} $:$...
Answer 1 To determine the exact values of the trigonometric functions for angle $ \frac{7\pi}{6} $, we follow these steps:1. Recognize that $ \frac{7\pi}{6} $ is in the third quadrant.2. Calculate the reference angle: $ \pi - \frac{7\pi}{6} =...
Answer 1 The unit circleAnswer 2 The coordinates of the point for $ heta = frac{3}{4} pi $ are found using:$ x = cosleft(frac{3}{4} pi ight) = -frac{sqrt{2}}{2} ext{ and } y = sinleft(frac{3}{4} pi ight) = frac{sqrt{2}}{2} $Thus, the coordinates...
Answer 1 To identify the quadrant where the angle $ \theta = \frac{3\pi}{4} $ lies, we need to examine the unit circle.$ \frac{3\pi}{4} $ is in radians.The angle $ \theta = \frac{3\pi}{4} $ is less than $ \pi $ but more than $ \frac{\pi}{2}...
Answer 1 To determine the quadrant of a point on the unit circle, consider the signs of the x and y coordinates:Quadrant I: Both coordinates are positive ($x > 0$, $y > 0$)Quadrant II: x is negative, y is positive ($x < 0$, $y > 0$)Quadrant III: Both...
Answer 1 To calculate $ \cos(\frac{\pi}{4}) $ using the unit circle, we look at the angle $ \frac{\pi}{4} $ on the unit circle.At this angle, both sine and cosine values are equal.Thus, the value of $ \cos(\frac{\pi}{4}) $ is:$ \cos(\frac{\pi}{4}) =...