9. Unit Circle

Reference Angles

9. Unit Circle

Reference Angles

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Multiple Choice

For each expression, identify which coterminal angle to use & determine the exact value of the expression.
$\cos\left(-\frac{10\pi}{4}\right)$

$0$

$1$

$-1$

$\frac{\sqrt2}{2}$

Verified step by step guidance

First, understand that coterminal angles are angles that share the same terminal side. To find a coterminal angle, you can add or subtract multiples of 2π from the given angle.

Start by simplifying the given angle: $-\frac{10\pi}{4}$. Simplify this fraction to $-\frac{5\pi}{2}$.

To find a positive coterminal angle, add 2π (or $\frac{4\pi}{2}$) to $-\frac{5\pi}{2}$ until the angle is positive. This gives $-\frac{5\pi}{2} + \frac{4\pi}{2} = -\frac{\pi}{2}$.

Now, find the cosine of $-\frac{\pi}{2}$. Recall that cosine is the x-coordinate on the unit circle. At $-\frac{\pi}{2}$, the point on the unit circle is (0, -1).

Thus, the cosine of $-\frac{\pi}{2}$ is 0. Therefore, the exact value of $\cos\left(-\frac{10\pi}{4}\right)$ is 0.

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Go to Practice

Struggling with Precalculus?

For each expression, identify which coterminal angle to use & determine the exact value of the expression.cos(−10π4)\cos\left(-\frac{10\pi}{4}\right)cos(−410π)

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Reference Angles practice set

For each expression, identify which coterminal angle to use & determine the exact value of the expression.
$\cos\left(-\frac{10\pi}{4}\right)$