Trigonometric Functions

10 Components
Initial Task
Remote Measures
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4
Formative Assessment Lesson
Ferris Wheel
Re-engagement
Re-engagement for Unit 3
End of Unit Assessments
End of Unit Assessment for Unit 3 End of Unit Assessment Teacher Resources ALG II Unit 3 Find aligned Regents questions with Quiz Banker
A2 U3: Trigonometric Functions
Browse Components
Initial Task
Remote Measures
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4
Formative Assessment Lesson
Ferris Wheel
Re-engagement
Re-engagement for Unit 3
End of Unit Assessments
End of Unit Assessment for Unit 3 End of Unit Assessment Teacher Resources ALG II Unit 3 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 2

A circle is symmetrical and its points are related by a center and radius.

1 week
See Standards
Common Core: Additional Standards:
F-TF.A.1

Extend the domain of trigonometric functions using the unit circle. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.C.8

Prove and apply trigonometric identities.  Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

Evidence of Understanding

  • describe the properties of a circle
    • explore the relationship between a center point and a fixed distance (radius) rotated around it
      • define a circle using the center, radius, and lines of symmetry
    • use tools to inductively show the circumference of a circle is 2πr
    • explain the relationship between the central angle of a circle and its arc measure
      • describe a circle using 360o degrees and 2π  radians or 180o and π radians
  • graph the equation of a circle in the coordinate plane
    • given any equation (x - h)2+ (y - k)2 = r2, describe how x, y, h, k, and r impact the graph
    • find the center and the radius of a circle by completing the square
    • given a coordinate point, use the graph or equation toprove if it lies on the circle
    • given a coordinate point, use symmetry to justify other points on the circle
    • use Pythagorean Theorem to identify the radius, center, or points that lie on the circle
      • explain the connection of the equation of a circle and Pythagorean Theorem
  • use triangles and trigonometry to describe the graph of a circle
    • given the center, radius and the terminal side of any angle between 0o  and 360o , find the coordinates of the corresponding point on the circle
      • use the properties of special right triangles (30-60-90 and 45-45-90)
      • describe the relationship between cosine and the x coordinate of a point on the circle
      • describe the relationship between sine and the y coordinate of a point on the circle
    • prove sin2 θ + cos2 θ = 1
    • use transformations to describe and justify the relationship between coordinate points that share a reference angle
      • Ex: the points at 30o  and 150o  are similar because the right triangle is reflected
      • Ex: the points 30o  and 120o  are similar because the right triangle is rotated   
    • given the center and any point on the circle, use inverse trig functions (sin-1, cos-1, and tan-1) to find the measure of the circle’s corresponding central angle

Develop conceptual understanding:

circle, circumference, arc measure, radian, terminal side, special right triangle (30-60-90 and 45-45-90), cosine, sine, reference angle

Supporting terms to communicate:

center, radius, central angle, degrees, symmetrical, reflect, completing the square, quadrant, Pythagorean Theorem, right triangle, reflection, rotation, inverse trig
Core Resource

A core resource supports multiple days of instruction.