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°

- use similarity, dilations, and scale factor to justify why a
**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**

- determine the angle of
- 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.

- determine when to use Pythagorean Theorem or trig ratios (or a combination of methods) to solve right triangles

Develop conceptual understanding:

trigonometric ratios, sine, cosine, tangent, special right triangle, inverse trig, angle of depression, angle of elevationSupporting terms to communicate:

constant ratio, similarity, scale factor, leg, side, opposite, adjacent, hypotenuse, corresponding, complementary, isosceles triangle