Find the values of $cos( heta)$ and $sin( heta)$ for $ heta = frac{5pi}{4}$
Answer 1
John Anderson
To find the values of $\cos(\theta)$ and $\sin(\theta)$ for $\theta = \frac{5\pi}{4}$, we start by locating the angle on the unit circle. The angle $\frac{5\pi}{4}$ is in the third quadrant.
In the third quadrant, both sine and cosine values are negative. The reference angle for $\frac{5\pi}{4}$ is $\pi/4$, for which the cosine and sine values are both $\frac{\sqrt{2}}{2}$.
Therefore:
$\cos\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$
$\sin\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$
Answer 2
Abigail Nelson
To solve for $cos( heta)$ and $sin( heta)$ where $ heta = frac{5pi}{4}$, follow these steps:
1. Identify the quadrant. The angle $ heta = frac{5pi}{4}$ is in the third quadrant where both sine and cosine are negative.
2. Determine the reference angle, which is $pi/4$. The values for sine and cosine at $pi/4$ are $frac{sqrt{2}}{2}$.
3. Apply the signs based on the quadrant:
$cosleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2}$
$sinleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2}$
Answer 3
Ella Lewis
For $ heta = frac{5pi}{4}$:
The reference angle is $pi/4$.
In the third quadrant, both sine and cosine are negative.
Thus:
$cosleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2}$
$sinleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2}$
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