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Answer 1 To determine the equation for a unit circle flipped over the y-axis, we start with the standard unit circle equation: $x^2 + y^2 = 1$ When we flip the unit circle over the y-axis, we change the sign of the x-coordinate. Therefore, the new...

Answer 1 To find the value of $\cos \theta$ on the unit circle, we use the unit circle definition where the coordinates are $(\cos \theta, \sin \theta)$. For $\theta = \pi/3$, the coordinates on the unit circle are: $\left( \cos \frac{\pi}{3}, \sin...

Answer 1 To solve for all angles \( \theta \) in the interval \([0, 2\pi)\) where \( \cos(\theta + \pi/6) = \sqrt{3}/2 \), we first identify the standard angles where cosine equals \( \sqrt{3}/2 \). These angles are: $\alpha = 0 \text{ or } \alpha =...

Answer 1 Given point $(-3, -4)$, we first calculate the radius r: $ r = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 $ In the unit circle, the radius (or hypotenuse) is 1. So, we need to normalize the coordinates to fit the unit circle. $ x...

Answer 1 Given the angle $ \theta = \frac{3\pi}{4} $, find the values of $ \sin \theta $, $ \cos \theta $, and $ \tan \theta $. Step 1: Identify the reference angle. The reference angle for $ \theta = \frac{3\pi}{4} $ is $ \frac{\pi}{4} $. Step 2:...

Answer 1 The coordinates of the point $P$ on the unit circle can be expressed as $P(\cos\theta, \sin\theta)$. To find the coordinates of the reflection of $P$ across the line $y=x$, we interchange the x and y coordinates of $P$. Therefore, the...