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Answer 1 To convert 225 degrees to radians, we use the conversion factor $\frac{\pi}{180}$:$225^\circ \times \frac{\pi}{180} = \frac{225\pi}{180} = \frac{5\pi}{4}$Next, identify the coordinates on the unit circle at $\frac{5\pi}{4}$ radians:The angle...

Answer 1 Given a point on the unit circle with polar coordinates $(r, \theta)$, where $r = 1$ and $\theta = \frac{5\pi}{6}$, find the Cartesian coordinates $(x, y)$.First, recall the conversion formulas from polar to Cartesian coordinates:$ x = r...

Answer 1 To find the exact values of $\sin(\theta)$ and $\cos(\theta)$ for $\theta = \frac{5\pi}{6}$, we use the unit circle. The angle $\frac{5\pi}{6}$ radians is in the second quadrant, where sine is positive and cosine is negative. The reference...

Answer 1 To convert degrees to radians, use the formula: $\text{radians} = \text{degrees} \times \frac{\pi}{180}$ Plugging in 120 degrees: $120^{\circ} \times \frac{\pi}{180} = \frac{120\pi}{180}$ Simplify the fraction: $\frac{120\pi}{180} =...

Answer 1 In order to memorize the unit circle, one effective method is to understand how it is derived from fundamental trigonometric principles. Let's start by deriving key points: We know the unit circle has a radius of 1. The key angles we need to...

Answer 1 To find the sine, cosine, and tangent values of the angle $225^{\circ}$ using the unit circle, follow these steps:1. Convert the angle to radians: $225^{\circ} = 225 \times \frac{\pi}{180} = \frac{5\pi}{4}$2. Determine the reference angle:...