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Answer 1 To find the sine and cosine values at $ t = \frac{\pi}{4} $ on the unit circle, we use the following values:$ \sin\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} $$ \cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} $Thus, the sine and...
Answer 1 To find the coordinates on the unit circle for $ \theta = \frac{\pi}{4} $, we use the unit circle properties.For $ \theta = \frac{\pi}{4} $, the coordinates are given by:$ (\cos(\frac{\pi}{4}), \sin(\frac{\pi}{4})) $From trigonometric...
Answer 1 To find the values of $\sin$ and $\cos$ at an angle of $\theta = \frac{\pi}{3}$ on the unit circle:$\sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$$\cos(\frac{\pi}{3}) = \frac{1}{2}$Answer 2 Consider $ heta = frac{pi}{4}$. The values of $sin$ and...
Answer 1 To find the angle $\theta$ in radians for a point on the unit circle where the $x$-coordinate is $\frac{1}{2}$, we consider the cosine function:$\cos(\theta) = \frac{1}{2}$The angles that satisfy this equation are:$\theta = \frac{\pi}{3}$...
Answer 1 To find the value of $ \sin(15^\circ) $ using the unit circle, we use the angle addition formula:$ \sin(a + b) = \sin(a) \cos(b) + \cos(a)\sin(b) $Here, let $ a = 45^\circ $ and $ b = -30^\circ $. Then,$ \sin(45^\circ - 30^\circ) =...
Answer 1 To solve for $ \tan(x) $ given $ \cos(x) = \frac{1}{2} $ on the unit circle, we must first determine the corresponding $ \sin(x) $. On the unit circle:$ \cos(x) = \frac{1}{2} $We know that at $ x = \frac{\pi}{3} $ and $ x = -\frac{\pi}{3} $,...