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Answer 1 First, recall that in the unit circle, an angle of 45 degrees corresponds to $\frac{\pi}{4}$ radians. From trigonometric identities: $\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$ $\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$ Therefore, the values...
Answer 1 To find the values of $\sin$, $\cos$, and $\tan$ at $45^\circ$ on the unit circle, we start by noting that $45^\circ$ is the same as $\frac{\pi}{4}$ radians. The coordinates of the point on the unit circle at $\frac{\pi}{4}$ radians are...
Answer 1 Given a point on the unit circle in the complex plane, represented by the complex number $z = e^{i\theta}$, determine the value of $\cos(\theta)$. Since $z = e^{i\theta}$, we know that: $z = \cos(\theta) + i\sin(\theta)$ Thus, the real part...
Answer 1 Given that $\theta$ is in the fourth quadrant and the point on the unit circle is $(\frac{1}{2}, -\frac{\sqrt{3}}{2})$, we can find the exact values of $\sin\theta$, $\cos\theta$, and $\tan\theta$. First, we recognize that $(\cos\theta,...
Answer 1 We know that at $45^\circ$, the coordinates on the unit circle are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.Therefore,$\sin 45^\circ = \frac{\sqrt{2}}{2}$$\cos 45^\circ = \frac{\sqrt{2}}{2}$To find $\tan 45^\circ$, we use the...
Answer 1 To find the sine and cosine of the angle $\theta = \frac{\pi}{4}$ on the unit circle, we use the coordinates of the point where the terminal side of the angle intersects the unit circle. The unit circle has a radius of 1, and for $\theta =...