
10.24 Functions on the Unit Circle
Authored by Kayla Hagerty Simmons
Mathematics
9th - 12th Grade
CCSS covered
Used 1+ times

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15 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
0
undefined
1
-1
Answer explanation
The secant function, \sec(x), is defined as \frac{1}{\cos(x)}. At \frac{3\pi}{2}, \cos\left(\frac{3\pi}{2}\right) = 0, making \sec\left(\frac{3\pi}{2}\right) undefined.
Tags
CCSS.HSF.TF.A.2
2.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Answer explanation
To find \( \sin\left(\frac{7\pi}{6}\right) \), note that \( \frac{7\pi}{6} \) is in the third quadrant where sine is negative. The reference angle is \( \frac{\pi}{6} \), giving \( \sin\left(\frac{7\pi}{6}\right) = -\frac{1}{2} \).
Tags
CCSS.HSF.TF.A.2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
undefined
0
1
-1
Answer explanation
The tangent function, \( \tan(x) \), is periodic with a period of \( \pi \). Thus, \( \tan(-3\pi) = \tan(0) = 0 \). Therefore, the correct answer is 0.
Tags
CCSS.HSF.TF.A.2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Answer explanation
The angle \( \frac{3\pi}{4} \) is in the second quadrant of the unit circle. The coordinates are given by \( \left( \cos \frac{3\pi}{4}, \sin \frac{3\pi}{4} \right) = \left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) \).
Tags
CCSS.HSF.TF.A.2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
I
II
III
IV
Answer explanation
The angle -\frac{2\pi}{3} radians is equivalent to 240 degrees, which lies in the third quadrant where both sine and cosine values are negative. Therefore, the correct answer is III.
Tags
CCSS.HSF.TF.A.2
6.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
What is the radius of a unit circle?
1
2
Answer explanation
A unit circle is defined as a circle with a radius of 1. Therefore, the correct answer is 1, as it represents the radius of a unit circle.
Tags
CCSS.HSF.TF.A.2
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Answer explanation
To find \( \csc\left(\frac{3\pi}{4}\right) \), we first find \( \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} \). The cosecant is the reciprocal, so \( \csc\left(\frac{3\pi}{4}\right) = \frac{1}{\sin\left(\frac{3\pi}{4}\right)} = \sqrt{2} \).
Tags
CCSS.HSF.TF.A.2
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