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Answer 1 To find the values of $ \sin $, $ \cos $, and $ \tan $ for the angle $ \frac{\pi}{4} $ on the unit circle, we use the unit circle properties:$ \sin \left( \frac{\pi}{4} \right) = \frac{ \sqrt{2} }{ 2 } $$ \cos \left( \frac{\pi}{4} \right) =...
Answer 1 LetAnswer 2 Using the unit circle, we can find the value of the tangent function for the angles $ heta = frac{pi}{4} $, $ heta = frac{3pi}{4} $, and $ heta = pi $: 1. For $ heta = frac{pi}{4} $: $ an(frac{pi}{4}) = 1 $ 2. For $ heta =...
Answer 1 Consider the unit circle centered at the origin $(0,0)$ in the coordinate plane. Given that $A$, $B$, and $C$ are angles in the unit circle, find $\sin(A)$, $\cos(B)$, and $\tan(C)$ if the following conditions are met: 1) $A = \pi/3$ 2) $B =...
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} =...