Find the sine and cosine values at different angles on the unit circle
Answer 1
Daniel Carter
Given the unit circle, find the sine and cosine values for the following angles:
1.
txt1
txt1
txt1
$ radians
2. $\frac{\pi}{4}$ radians
3. $\frac{\pi}{2}$ radians
1. At
txt1
txt1
txt1
$ radians, the coordinates are $(1, 0)$, so the sine value is
txt1
txt1
txt1
$ and the cosine value is $1$.
2. At $\frac{\pi}{4}$ radians, the coordinates are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$, so the sine value is $\frac{\sqrt{2}}{2}$ and the cosine value is $\frac{\sqrt{2}}{2}$.
3. At $\frac{\pi}{2}$ radians, the coordinates are $(0, 1)$, so the sine value is $1$ and the cosine value is
txt1
txt1
txt1
$.
Answer 2
Michael Moore
Given the unit circle, find the sine and cosine values for the following angles:
1.
txt2
txt2
txt2
$ radians
2. $frac{pi}{4}$ radians
3. $frac{pi}{2}$ radians
1. At
txt2
txt2
txt2
$ radians, the sine value is
txt2
txt2
txt2
$ and the cosine value is $1$.
2. At $frac{pi}{4}$ radians, the sine value is $frac{sqrt{2}}{2}$ and the cosine value is $frac{sqrt{2}}{2}$.
3. At $frac{pi}{2}$ radians, the sine value is $1$ and the cosine value is
txt2
txt2
txt2
$.
Answer 3
Amelia Mitchell
On the unit circle, at
txt3
txt3
txt3
$ radians, sine is
txt3
txt3
txt3
$ and cosine is $1$; at $frac{pi}{4}$ radians, both sine and cosine are $frac{sqrt{2}}{2}$; at $frac{pi}{2}$ radians, sine is $1$ and cosine is
txt3
txt3
txt3
$.
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