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Answer 1 To find the coordinates on the unit circle where the tangent line is horizontal, we first recall that the unit circle is defined by the equation: $ x^2 + y^2 = 1 $ The slope of the tangent line to the circle at any point (x, y) is given by...
Answer 1 The coordinates of $ \frac{3\pi}{4} $ on the unit circle can be found using the unit circle definitions. The angle $ \frac{3\pi}{4} $ corresponds to $ 135^{\circ} $. At this angle, the coordinates are: $ \left( -\frac{\sqrt{2}}{2},...
Answer 1 To find the sine and cosine of $ \frac{7\pi}{6} $ on the unit circle, we first determine the reference angle. The reference angle for $ \frac{7\pi}{6} $ is $ \frac{\pi}{6} $.The sine and cosine of $ \frac{7\pi}{6} $ correspond to the sine...
Answer 1 To find the sine and cosine of $150^\circ$, we first identify its reference angle:The reference angle for $150^\circ$ is:$180^\circ - 150^\circ = 30^\circ$The sine and cosine of $30^\circ$ are:$ \sin(30^\circ) = \frac{1}{2} $$ \cos(30^\circ)...
Answer 1 The equation of the unit circle is:\n $ x^2 + y^2 = 1 $\n To find the inverse, we use the transformation:\n $ z = \x0crac{1}{x + yi} $\n where $ z = u + vi $ and $ x + yi = \x0crac{1}{u - vi} $.\n Therefore, the inverse relation in terms of...