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**Standard(s): **
[MA2015] GEO (9-12) 20 :

[MA2015] GEO (9-12) 21 :

[MA2019] GEO-19 (9-12) 35 :

20 ) Explain and use the relationship between the sine and cosine of complementary angles. [G-SRT7]

[MA2015] GEO (9-12) 21 :

21 ) Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [G-SRT8]

[MA2019] GEO-19 (9-12) 35 :

35. Discover and apply relationships in similar right triangles.

a. Derive and apply the constant ratios of the sides in special right triangles (45^{o}-45^{o}-90^{o} and 30^{o}-60^{o}-90^{o}).

b. Use similarity to explore and define basic trigonometric ratios, including sine ratio, cosine ratio, and tangent ratio.

c. Explain and use the relationship between the sine and cosine of complementary angles.

d. Demonstrate the converse of the Pythagorean Theorem.

e. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including finding areas of regular polygons.

Students begin the study of trigonometry in the final topic of the module. The emphasis in the module on side length relationships within similar triangles (Topic C) and the specific emphasis on right triangles

(Topic D) help set the foundation for trigonometry. Lesson 25 is the last highlight of the side length ratios within and between right triangles. Students are guided to the idea that the values of the ratios depend solely on a given acute angle in the right triangle before the basic trigonometric ratios are explicitly defined in Lesson 26 (G.SRT.C.6). After practice with ratios labeled as (Lesson 21) and (Lesson 25), students are introduced to the trigonometric ratios sine, cosine, and tangent (G-SRT.C.6) in Lesson 26. Students examine the relationship between sine and cosine in Lesson 27, discovering that the sine and cosine of complementary angles are equal (G-SRT.C.7). They are also introduced to the common sine and cosine values of angle measures frequently seen in trigonometry. Students apply the trigonometric ratios to solve for unknown lengths in Lessons 28 and 29; students also learn about the relationship between tangent and slope in Lesson 29 (G-SRT.C.8). In Lesson 30, students use the Pythagorean theorem to prove the identity and also show why. In Lessons 31–33, students study the application of trigonometry to determine area and solve for unknown lengths using the laws of sines and cosines (G-SRT.9, G-SRT.10, G-SRT.11). Finally, in Lesson 34, students learn how to determine the unknown measure of an angle of a right triangle. Students are introduced to the trigonometric functions and These inverse functions are taught formally in Algebra II. For now, students should understand the meaning of and how to use and to determine unknown measures of angles.