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Answer 1 To find the points on the unit circle where the tangent line passes through the point $(1, 2)$, we can use the following steps: 1. The equation of the unit circle is given by $x^2 + y^2 = 1$. 2. The slope of the tangent line at any point...
Answer 1 To determine the sine of $ \frac{\pi}{4} $ on the unit circle, recall that the coordinates for $ \frac{\pi}{4} $ are:$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $The y-coordinate gives you the sine value:$ \sin\left(...
Answer 1 In the unit circle, if the $\sin(\theta)$ is negative, it means that the angle $\theta$ is in the third or fourth quadrant. In both of these quadrants, the sine value is negative. Cosine values in these quadrants can be positive (fourth...
Answer 1 To find the position of $ -\frac{\pi}{2} $ on a unit circle, we start by understanding that the unit circle is a circle with radius 1 centered at the origin (0,0). The angle $ -\frac{\pi}{2} $ is measured in the clockwise direction from the...
Answer 1 To determine the values of $ \theta $ where $ \sin(\theta) $ and $ \cos(\theta) $ are equal in the flipped unit circle, we start by setting up the equation:$ \sin(\theta) = \cos(\theta) $ Dividing both sides by $ \cos(\theta) $, we get:$...
Answer 1 To determine the quadrant of the angle $ \frac{\pi}{3} $, we note that this angle is equivalent to 60 degrees.In the unit circle, angles between 0 and 90 degrees are in the first quadrant.Therefore, the angle $ \frac{\pi}{3} $ is in the...