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Answer 1 To find the cosine and sine of the angle $\frac{\pi}{4}$ on the unit circle, we need to recall the coordinates of the point where the terminal side of the angle intersects the unit circle.For the angle $\frac{\pi}{4}$, both the x-coordinate...
Answer 1 To find the cotangent of $ \frac{\pi}{4} $ on the unit circle, we use the definition of cotangent in terms of sine and cosine. $ \cot \theta = \frac{\cos \theta}{\sin \theta} $ For $ \theta = \frac{\pi}{4} $, both $ \sin \frac{\pi}{4} $ and...
Answer 1 First, we find the coordinates of the point on the unit circle corresponding to $\theta = \frac{2\pi}{3}$. The coordinates are $\left( -\frac{1}{2}, \frac{\sqrt{3}}{2} \right)$. Since $\sec(\theta) = \frac{1}{\cos(\theta)}$, we have:...
Answer 1 $\text{Consider the point where the angle is } 60^\circ \text{ on the unit circle.}$ $\text{The cosine of } 60^\circ \text{ is given by } \cos(60^\circ) = \frac{1}{2}. $$\text{Therefore, the cosine value at } 60^\circ \text{ on the unit...
Answer 1 First, locate the angle $\frac{5\pi}{6}$ on the unit circle.The angle $\frac{5\pi}{6}$ is in the second quadrant.In the second quadrant, sine is positive and cosine is negative.The reference angle for $\frac{5\pi}{6}$ is $\pi -...
Answer 1 Consider the angle $\theta = \frac{3\pi}{4}$ on the unit circle.First, determine the reference angle. The reference angle for $\frac{3\pi}{4}$ is $\frac{\pi}{4}$.Since $\frac{3\pi}{4}$ is in the second quadrant, tangent is negative.We know...