$ ext{Find the sine and cosine of a 45-degree angle}$
Answer 1
Alex Thompson
To find the sine and cosine of a 45-degree angle, we can use the unit circle. A 45-degree angle corresponds to $\frac{\pi}{4}$ radians.
On the unit circle, the coordinates for $\frac{\pi}{4}$ are given by $\left( \cos \frac{\pi}{4}, \sin \frac{\pi}{4} \right)$.
We know from trigonometric identities that:
$\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$
$\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$
Therefore, the sine and cosine of a 45-degree angle are both $\frac{\sqrt{2}}{2}$.
Answer 2
Benjamin Clark
To determine the sine and cosine values for a 45-degree angle, we can refer to the unit circle. A 45-degree angle is the same as $frac{pi}{4}$ radians.
The unit circle shows that the coordinates for $frac{pi}{4}$ are $left( cos frac{pi}{4}, sin frac{pi}{4}
ight)$.
From trigonometric properties:
$cos frac{pi}{4} = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$
$sin frac{pi}{4} = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$
Thus, both sine and cosine of 45 degrees equal $frac{sqrt{2}}{2}$.
Answer 3
Isabella Walker
For a 45-degree angle, which is $frac{pi}{4}$ radians:
$cos frac{pi}{4} = frac{sqrt{2}}{2}$
$sin frac{pi}{4} = frac{sqrt{2}}{2}$
Hence, $cos 45^circ$ and $sin 45^circ$ are both $frac{sqrt{2}}{2}$.
Start Using PopAi Today