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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...
Answer 1 To find the trigonometric values of an angle of 150 degrees on the unit circle, we can use the angle relationship and symmetry of the unit circle. 1. Convert the angle to radians: $150° = \frac{5\pi}{6}$ radians. 2. Recall that on the unit...