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

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Trig Functions and The Unit Circle

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

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