Trigonometric Relationships - Lesson Plan

[b]Standard[br][/b]Ma.912.T.1 Define and use trigonometric ratios, identities, or functions to solve problems.[br][b]Benchmark[br][/b]MA.912.T.1.1 Define trigonometric ratios for acute angles in right triangles.[b][br][br]Learning Target[br][/b]Students will be able to determine trigonometric ratios using the coordinate plane.[br][b][br]Materials[br][/b]Computer/chromebook/tablet[br]Scientific calculator[b][br][br]Introduction/Warm-up[br][/b]Have students find Sine, Cosine, and Tangent of the following triangle using [math]\angle PAG[/math] as the reference angle. 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[/img][br]Students may need a reminder of sine = opposite/hypotenuse, cosine = adjacent/hypotenuse and tangent = opposite/adjacent.[br][b][br]Guided Instruction/Exploration[br][/b]Using the GeoGebra Applet, have students work with a partner to find three similar triangles in the coordinate plane. Students will record the x, y, hypotenuse, sin(a), cos(a), and tan(a) of each triangle found. Ask students what they notice.
Guide students to the conclusion that similar triangles have the same cosine, sine, and tangent.[b][br][br]Guided Practice[br][/b]Using the triangles they found, have students work with their partner to find the three ratios (cosine, sine, and tangent) for each triangle EXACTLY using [i]a [/i]as the reference angle. This will require them to find the length of the hypotenuse using the Pythagorean Theorem. Compare their answers with what they found using the applet.[br][br]Come back together as a class and complete the attached Practice Worksheet.
Trigonometric Ratio Practice Worksheet
[b]Independent Practice/Homework[br][/b]Students will complete the following Trigonometric Ratio Homework.
Trigonometric Ratio Homework

Information: Trigonometric Relationships - Lesson Plan