Answer 1 To find the sine and cosine of $ \frac{\pi}{4} $ using the unit circle:On the unit circle, the angle $ \frac{\pi}{4} $ corresponds to the coordinates $ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $.Therefore,$ \sin\left(...

Answer 1 To find the coordinates of a point on the unit circle at an angle of \( \frac{\pi}{4} \), we use the unit circle definition:\n The unit circle is defined as all points (x, y) such that:\n $ x^2 + y^2 = 1 $\n For an angle \( \theta \), the...

Answer 1 To find the tangent of the angle $ \theta $ on a unit circle, one must understand that the tangent of an angle is defined as the ratio of the sine to the cosine of that angle: $ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $ For example,...

Answer 1 First, recognize that $2\sin(x)\cos(x) = \sin(2x)$. Thus, the equation becomes: $\sin(2x) = 1$ The solution for $\sin(2x) = 1$ occurs at: $2x = \frac{\pi}{2} + 2k\pi$, where $k$ is any integer. Thus: $x = \frac{\pi}{4} + k\pi$ For $k = 0$:...

Answer 1 To find the coordinates of a point on the negative unit circle given a specific angle $ \theta $, we use the equation of the unit circle: $ x^2 + y^2 = 1 $ The coordinates can be found using parametric equations: $ x = -\cos(\theta) $ $ y =...