What are the sine, cosine, and tangent of the angle $frac{pi}{4}$ on the unit circle?
Answer 1
Chloe Evans
To find the sine, cosine, and tangent of the angle $\frac{\pi}{4}$ on the unit circle, we need to locate the angle on the circle.
The angle $\frac{\pi}{4}$ radians is equivalent to 45 degrees. In the unit circle, this corresponds to the point where both x and y coordinates are equal, as the angle bisects the first quadrant.
The coordinates of the point are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.
Therefore:
$ \sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $
$ \cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $
$ \tan \left( \frac{\pi}{4} \right) = \frac{ \frac{\sqrt{2}}{2} }{ \frac{\sqrt{2}}{2} } = 1 $
Answer 2
Ella Lewis
The angle $frac{pi}{4}$ is 45 degrees. On the unit circle, this angle corresponds to the point $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
The sine of the angle is the y-coordinate of this point, which is $frac{sqrt{2}}{2}$.
The cosine of the angle is the x-coordinate of this point, which is also $frac{sqrt{2}}{2}$.
The tangent of the angle is the ratio of the sine to the cosine:
$ an left( frac{pi}{4}
ight) = frac{ sin left( frac{pi}{4}
ight) }{ cos left( frac{pi}{4}
ight) } = frac{ frac{sqrt{2}}{2} }{ frac{sqrt{2}}{2} } = 1 $
Answer 3
Christopher Garcia
For the angle $frac{pi}{4}$ radians, the sine and cosine are both $frac{sqrt{2}}{2}$, and the tangent is 1.
$ sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ an left( frac{pi}{4}
ight) = 1 $
Start Using PopAi Today