Find the sine and cosine values at different points on the unit circle.
Answer 1
Lily Perez
To find the sine and cosine values at different points on the unit circle, we can use the angle in radians.
1. For the angle $\frac{\pi}{6}$ radians:
The coordinates on the unit circle are $\left( \cos \frac{\pi}{6}, \sin \frac{\pi}{6} \right)$.
Thus, we get: $\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}$ and $\sin \frac{\pi}{6} = \frac{1}{2}$.
2. For the angle $\frac{\pi}{4}$ radians:
The coordinates on the unit circle are $\left( \cos \frac{\pi}{4}, \sin \frac{\pi}{4} \right)$.
Thus, we get: $\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$ and $\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$.
3. For the angle $\frac{\pi}{3}$ radians:
The coordinates on the unit circle are $\left( \cos \frac{\pi}{3}, \sin \frac{\pi}{3} \right)$.
Thus, we get: $\cos \frac{\pi}{3} = \frac{1}{2}$ and $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$.
Answer 2
Joseph Robinson
To determine the sine and cosine values at specific points on the unit circle, we look at the angles in radians.
1. For the angle $frac{pi}{6}$ radians, the coordinates are $left( cos frac{pi}{6}, sin frac{pi}{6}
ight)$.
Thus, $cos frac{pi}{6} = frac{sqrt{3}}{2}$ and $sin frac{pi}{6} = frac{1}{2}$.
2. For the angle $frac{pi}{4}$ radians, the coordinates are $left( cos frac{pi}{4}, sin frac{pi}{4}
ight)$.
Thus, $cos frac{pi}{4} = frac{sqrt{2}}{2}$ and $sin frac{pi}{4} = frac{sqrt{2}}{2}$.
3. For the angle $frac{pi}{3}$ radians, the coordinates are $left( cos frac{pi}{3}, sin frac{pi}{3}
ight)$.
Thus, $cos frac{pi}{3} = frac{1}{2}$ and $sin frac{pi}{3} = frac{sqrt{3}}{2}$.
Answer 3
Samuel Scott
Find the sine and cosine values for:
1. $frac{pi}{6}$ radians: $cos frac{pi}{6} = frac{sqrt{3}}{2}, sin frac{pi}{6} = frac{1}{2}$.
2. $frac{pi}{4}$ radians: $cos frac{pi}{4} = frac{sqrt{2}}{2}, sin frac{pi}{4} = frac{sqrt{2}}{2}$.
3. $frac{pi}{3}$ radians: $cos frac{pi}{3} = frac{1}{2}, sin frac{pi}{3} = frac{sqrt{3}}{2}$.
Start Using PopAi Today