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Answer 1 The unit circle is defined as the set of all points in the coordinate plane that are exactly one unit away from the origin. The equation of the unit circle can be derived using the Pythagorean theorem. For a point $(x, y)$ on the circle:$...
Answer 1 To find the coordinates of the point on the unit circle at angle $ \frac{7\pi}{6} $, use the unit circle values:$ \frac{7\pi}{6} $ is in the third quadrant, where both sine and cosine are negative. The reference angle is $ \frac{\pi}{6} $,...
Answer 1 To find the equation of the tangent line to the circle at the point $(3, 4)$, follow these steps:\nThe equation of the circle is:\n$ x^2 + y^2 = 25 $\nThe gradient of the radius at the point $(3, 4)$ is:\n$ \x0crac{4 - 0}{3 - 0} =...
Answer 1 To find θ in degrees, we first find the angle whose coordinates on the unit circle are closest to (1/2, -√3/2). This point corresponds to the angle -60 degrees or 300 degrees. The point (cos(θ), sin(θ)) that is closest must satisfy the...
Answer 1 Given the point $ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) $ on the unit circle, we need to find the secant of the corresponding angle $ \theta $. Recall that $ \sec(\theta) = \frac{1}{\cos(\theta)} $ and $ \cos(\theta) $ is the...
Answer 1 The unit circle is a circle with a radius of 1 centered at the origin (0, 0). The coordinates of a point on the unit circle with an angle $ \frac{\pi}{4} $ are found using trigonometric functions:$ x = \cos \left( \frac{\pi}{4} \right) =...