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Answer 1 The unit circle is the circle of radius 1 centered at the origin (0, 0) in the coordinate plane. The coordinates of any point on the unit circle can be determined using trigonometric functions, specifically sine and cosine.Given an angle...
Answer 1 The unit circle helps us to memorize common angle values. For $ \frac{\pi}{4} $, the coordinates are the same for both sine and cosine.$ \sin\left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $$ \cos\left( \frac{\pi}{4} \right) =...
Answer 1 The unit circle has a radius of 1. The coordinates of a point on the unit circle can be found using the formulas:$ x = \cos(\theta) $$ y = \sin(\theta) $For $ \theta = \frac{\pi}{4} $:$ x = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}...
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 =...