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Answer 1 The equation of the unit circle is given by:$x^2 + y^2 = 1$We are given that the x-coordinate is $\frac{1}{2}$. Substituting $x = \frac{1}{2}$ into the equation:$\left(\frac{1}{2}\right)^2 + y^2 = 1$$\frac{1}{4} + y^2 = 1$Subtract...
Answer 1 To determine the coordinates of a point on the unit circle for a given angle $\theta$, we use the fact that the unit circle has a radius of 1 and the coordinates can be expressed as $(\cos(\theta), \sin(\theta))$. Let's find the coordinates...
Answer 1 Given the angle $ \theta = \frac{2\pi}{3} $ radians, calculate $ \sin(\theta) $, $ \cos(\theta) $, and $ \tan(\theta) $. Solution: First convert the angle to degrees to understand its position on the unit circle: $\theta = \frac{2\pi}{3} $...
Answer 1 To find the value of $\csc(\theta + i \phi)$ on the unit circle, we first recall that $\csc(z) = \frac{1}{\sin(z)}$ and we utilize the definition of the sine function for complex arguments.Given $z = \theta + i \phi$, we have: $\sin(z) =...