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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) =...
Answer 1 To find the exact values of $ \sin(x) $, $ \cos(x) $, and $ \tan(x) $ for $ x = \frac{7\pi}{6} $, follow these steps:The angle $ \frac{7\pi}{6} $ is in the third quadrant.For the sine function:$ \sin\left(\frac{7\pi}{6}\right) =...
Answer 1 At the angle $ \frac{\pi}{4} $, the coordinates on the unit circle are: $ \left( \cos\left( \frac{\pi}{4} \right), \sin\left( \frac{\pi}{4} \right) \right) $ Using the unit circle values: $ \cos\left( \frac{\pi}{4} \right) =...