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This printable supports Common Core Mathematics Standard HSF-TF.A.2

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# Trig Functions and The Unit Circle (Grades 11-12)

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## Trig Functions and The Unit Circle

1.
Angle $theta$ is the angle in standard position whose terminal arm intersects the unit circle (centered at the origin) at the point $(7/12, sqrt(95)/12)$. What is the value of $sin(theta) ?$
1. $sqrt(95)/12$
2. $7/12$
3. $7/sqrt(95)$
4. $sqrt(95)/7$
2.
Angle A is in standard position. It's terminal arm intersects the unit circle at $(-3/10, sqrt(91)/10)$. What is the value of $cos(A) ?$
1. $-3/sqrt(91)$
2. $-sqrt(91)/3$
3. $sqrt(91)/10$
4. $-3/10$
3.
For the point $(5/7, (2sqrt(6))/7)$ on the unit circle centered at the origin, let angle $theta$ be the angle in standard position whose terminal arm intersects this point after the angle has made between 2 and 3 full rotations around the origin. What is the value of $cos(theta) ?$
1. $(2sqrt(6))/7$
2. $5/7$
3. $5/(2sqrt(6))$
4. $(2sqrt(6))/5$
4.
Point M, $(4/5, -3/5)$, is on the unit circle centered at the origin. The angle $theta$ is in standard position, with its terminal arm passing through point M. What is the value of $tan(theta) ?$
1. $-3/5$
2. $4/5$
3. $-4/3$
4. $-3/4$
5.
Angle $theta$ is the angle in standard form whose terminal arm passes through the point $(-5/13, -12/13)$ (which lies on the unit circle centered at the origin). What is the value of $tan(\theta) ?$
1. $12/5$
2. $5/12$
3. $-5/13$
4. $-12/13$
6.
Point P is a point on the unit circle centered at the origin whose coordinates are $( (2sqrt(3))/5, -sqrt(13)/5)$. The angle $theta$ is the angle in standard form that has made between 4 and 5 full rotations around the origin, counterclockwise, and whose terminal arm intersects point P. What is the value of $sin(theta) ?$
1. $sqrt(39)/6$
2. $(2sqrt(39))/13$
3. $(2sqrt(3))/5$
4. $-sqrt(13)/5$
7.
Let circle O be the unit circle centered about the origin. Let $(1/2,sqrt(3)/2)$ be point A, which is on the unit circle. Let $theta$ be the acute angle in standard position whose terminal arm passes through point A.
A.
What is the value of $sin(theta) ?$
1. $sqrt(3)$
2. $1/sqrt(3)$
3. $sqrt(3)/2$
4. $1/2$
B.
What is the value of $theta ?$
1. $pi/6$
2. $pi/3$
3. $pi/4$
4. $pi/2$
C.
What is the relationship between point A on circle O, its associated angle $theta$, and the ordered pair $(pi/3, sqrt(3)/2)$ of the function $f(x) = sin(x) ?$
1. The angle $theta$ is the first value of the ordered pair, and the y-value of point A is the second value.
2. The y-value of point A is the second value of the ordered pair. The first value of the ordered pair is the complement of $theta$.
3. The y-value of point A is the second value of the ordered pair. The first value of the ordered pair is random (it has no relationship to point A or $theta$).
4. There is no relationship.
D.
The following are ordered pairs of the function $f(x)=sin(x):$ $(pi/6, 1/2), ((13pi)/6, 1/2), ((25pi)/6, 1/2)$. To which point(s) on the unit circle would these ordered pairs be associated with, according to the relationship in the previous question.
1. $(sqrt(3)/2, 1/2)$
2. $(sqrt(3)/2, 1/2), (sqrt(2)/2, sqrt(2)/2), (1/2, sqrt(3)/2)$
3. $(sqrt(3)/2, 1/2), (-sqrt(3)/2, 1/2), (-sqrt(3)/2, -1/2)$
4. $(1/2, sqrt(3)/2)$
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