Big Idea:

Big Idea 2

Sine, Cosine, and Tangent are constant ratios that relate the angles and sides of a right triangle.

1 week

Evidence of Understanding

  • analyze characteristics of trigonometric ratios using right triangles
    • use similarity, dilations, and scale factor to justify why a trigonometric ratio is constant
    • analyze the legs of a right triangle to describe sine and cosine
      • use the definition of the sine or cosine ratio to explain why neither value can exceed 1
      • describe how increasing or decreasing one leg impacts the sine or cosine value
      • explain how the sine and cosine of complementary angles are related and create an algebraic expression that generalizes the relationship between sine and cosine
    • analyze the legs of a right triangle to describe the tangent
      • use the definition of the tangent ratio to explain why the tangent values increases without limit as the angle increases
      • describe features of a right triangle whose tangent is 1 (isosceles, 45-45-90)
      • explain why the tangent of 45° is always 1
    • use examples and nonexamples to make conjectures about special right triangles
      • the short side of a 30-60-90 triangle is always half the length of the hypotenuse
      • the sine of 30° is always ½ and, conversely,  if the sine is ½ then the angle is 30°
      • the cosine of 60° is always ½ and, conversely,  if the cosine is ½ then the angle is 60°
         
  • determine the measure of angles or sides using right triangles and trigonometric ratios
    • determine when to use Pythagorean Theorem or trig ratios (or a combination of methods) to solve right triangles
      • create diagrams and write equations to model situations using right triangles
      • recognize Pythagorean Theorem cannot be used to determine an unknown angle
    • find the value of an unknown angle using inverse trig functions (sin-1, cos-1, and tan-1)
      • determine the angle of depression or angle of elevation
    • use special triangle patterns (30-60-90 and 45-45-90) to determine a missing measure
    • find the area or perimeter of a simple polygon with right triangles using a variety of methods including trig, Pythagorean Theorem, special triangles, etc.

Develop conceptual understanding:

trigonometric ratios, sine, cosine, tangent, special right triangle, inverse trig, angle of depression, angle of elevation

Supporting terms to communicate:

constant ratio, similarity, scale factor, leg, side, opposite, adjacent, hypotenuse, corresponding, complementary, isosceles triangle
Core Resource
A core resource supports multiple days of instruction.
  • Introducing Right Triangles
    This single-day resource motivates the need for right-angle trigonometry.
    Resource:
    Introducing Right Triangles

    The objective for this initial introduction is to motivate the use of right-angle trigonometry through an investigation followed by a problem solving task using the results of that investigation.

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