Mathematics | Course : Model Geometry (Traditional Pathway)
Domain - Similarity, Right Triangles, and Trigonometry
Cluster - Define trigonometric ratios and solve problems involving right triangles.
[GEO.G-SRT.C.6] - Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- Ratio
A relationship between quantities such that for every a units of one quantity there are b units of the other. A ratio is often denoted by a:b and read “a to b”.
[GEO.G-SRT.A.3] -
Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
[GEO.G-SRT.C.7] -
Explain and use the relationship between the sine and cosine of complementary angles.
[GEO.G-SRT.C.8] -
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
[GEO.G-SRT.D.10] -
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
[AII.F-TF.A.2] -
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
[AII.F-TF.C.8] -
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.
[PC.F-TF.C.9] -
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
[PC.G-SRT.D.9] -
(+) Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
[PC.G-SRT.D.10] -
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
[AQR.F-TF.C.9] -
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.