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Answer 1 Given the angle $\theta = \frac{\pi}{3}$, find the coordinates of the corresponding point on the flipped unit circle where the x and y coordinates are switched.The standard coordinates for $\theta = \frac{\pi}{3}$ on the unit circle are...
Answer 1 To find the tan value for the angle $ \theta = \frac{\pi}{4} $ on the unit circle, we use the fact that $ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $. The sine and cosine values for $ \theta = \frac{\pi}{4} $ are both $...
Answer 1 To find the coordinates of the point on the unit circle corresponding to an angle of $120^{\circ}$, we first convert the angle to radians. The conversion formula is:$ \theta (\text{radians}) = \theta (\text{degrees}) \times \frac{\pi}{180}...
Answer 1 First, let's determine the reference angle for $\frac{7\pi}{4}$. We know that: $\frac{7\pi}{4} = 2\pi - \frac{\pi}{4}$ So, the reference angle is: $\frac{\pi}{4}$ Next, we find the value of $\tan(\frac{7\pi}{4})$. Since $\frac{7\pi}{4}$ is...
Answer 1 Given the angle θ = 45°, determine which quadrant of the unit circle the terminal side of the angle lies in. Solve: First, convert the angle to radians if necessary. For 45°, the equivalent in radians is $ \frac{\pi}{4} $. Since $...
Answer 1 To find the cosine and sine values for $\frac{5\pi}{6}$ radians in the unit circle, we start by recognizing that $\frac{5\pi}{6}$ is in the second quadrant.In the second quadrant, the angle is $\pi - \theta$. Here, $\theta =...