3. Unit Circle

Reference Angles

3. 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

Step 1: 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.

Step 2: Simplify the given angle $-\frac{10\pi}{4}$ by reducing the fraction. Divide both the numerator and the denominator by 2 to get $-\frac{5\pi}{2}$.

Step 3: Find a coterminal angle by adding 2π to $-\frac{5\pi}{2}$. This is equivalent to adding $\frac{4\pi}{2}$ to $-\frac{5\pi}{2}$, resulting in $-\frac{5\pi}{2} + \frac{4\pi}{2} = -\frac{\pi}{2}$.

Step 4: Recognize that $-\frac{\pi}{2}$ is a standard angle on the unit circle. The cosine of $-\frac{\pi}{2}$ is 0, as it corresponds to the point (0, -1) on the unit circle.

Step 5: Conclude that the exact value of $\cos\left(-\frac{10\pi}{4}\right)$ is 0, based on the coterminal angle $-\frac{\pi}{2}$.

5:31m

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Reference Angles practice set

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Struggling with Trigonometry?

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.
$\cos\left(-\frac{10\pi}{4}\right)$