Find the values of $sin( heta)$, $cos( heta)$, and $ an( heta)$ using the unit circle for $ heta = 135°$.
Answer 1
Emma Johnson
We start by locating the angle $\theta = 135°$ on the unit circle.
Since $135°$ is in the second quadrant, we use the reference angle $45°$ to find the values. The coordinates of the point on the unit circle at this angle are $\left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.
Thus, $\sin(135°) = \frac{\sqrt{2}}{2}$, $\cos(135°) = -\frac{\sqrt{2}}{2}$, and $\tan(135°) = \frac{\sin(135°)}{\cos(135°)} = \frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = -1$.
$\sin(135°) = \frac{\sqrt{2}}{2}$
$\cos(135°) = -\frac{\sqrt{2}}{2}$
$\tan(135°) = -1$
Answer 2
Ella Lewis
To determine $sin(135°)$, $cos(135°)$, and $ an(135°)$, we use the unit circle properties.
In the second quadrant, the angle $135°$ has a reference angle of $45°$. The sine and cosine values for $45°$ are $frac{sqrt{2}}{2}$.
Therefore, $sin(135°) = frac{sqrt{2}}{2}$ and $cos(135°) = -frac{sqrt{2}}{2}$ since cosine is negative in the second quadrant. Using the definition of tangent, $ an(135°) = frac{sin(135°)}{cos(135°)} = frac{frac{sqrt{2}}{2}}{-frac{sqrt{2}}{2}} = -1$.
$sin(135°) = frac{sqrt{2}}{2}$
$cos(135°) = -frac{sqrt{2}}{2}$
$ an(135°) = -1$
Answer 3
Lucas Brown
The angle $135°$ is in the second quadrant with a reference angle of $45°$.
From the unit circle, $sin(135°) = frac{sqrt{2}}{2}$, $cos(135°) = -frac{sqrt{2}}{2}$, and $ an(135°) = -1$.
$sin(135°) = frac{sqrt{2}}{2}$
$cos(135°) = -frac{sqrt{2}}{2}$
$ an(135°) = -1$
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